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1
RADAELLI, PAOLO. « La Regressione Lineare con i Valori Assoluti ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2004. http://hdl.handle.net/10281/2290.
Texte intégralRésumé :
The estimation of regression coefficients in the linear model is usually provided by least squares (LS) minimizing the sum of the squares of residuals. An alternative estimator is obtained by minimizing the sum of absolute residuals (MSAE) and was first introduced by Boscovich in 1757 for the straight line. We first provide a short historical background and then we show in detail, from a descriptive point of view, how to obtain the median regression (MSAE) coefficients for the straight line and, for the more general case of the hyperplane, the formulation of the problem as a linear programming problem. Defining the sample quantiles as a solution of a minimization problem, quantile regression, introduced by Koenker and Bassett (1978) provides an extension of this methodology in order to obtain regression coefficients of the hyperplane for a generic quantile of the dependent variable.We introduce quantile regression showing that the use of different loss functions: quadratic, absolute and asymmetric absolute leads respectively to least squares, median and quantile regression. In this thesis we extend these results to the linear regression for quantity quantiles. We first show that quantity quantiles can be defined as the solution to a minimization problem and then we extend the result to the linear regression framework. We finally deal with another use of absolute values in the regression context, in particular we consider the problem of the estimation of the regression coefficients by minimizing the Gini mean difference of the residuals; we show that this apporach fall in the class of R-estimators.
2
Guo, Mengmeng. « Generalized quantile regression ». Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2012. http://dx.doi.org/10.18452/16569.
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Die generalisierte Quantilregression, einschließlich der Sonderfälle bedingter Quantile und Expektile, ist insbesondere dann eine nützliche Alternative zum bedingten Mittel bei der Charakterisierung einer bedingten Wahrscheinlichkeitsverteilung, wenn das Hauptinteresse in den Tails der Verteilung liegt. Wir bezeichnen mit v_n(x) den Kerndichteschätzer der Expektilkurve und zeigen die stark gleichmßige Konsistenzrate von v-n(x) unter allgemeinen Bedingungen. Unter Zuhilfenahme von Extremwerttheorie und starken Approximationen der empirischen Prozesse betrachten wir die asymptotischen maximalen Abweichungen sup06x61 |v_n(x) − v(x)|. Nach Vorbild der asymptotischen Theorie konstruieren wir simultane Konfidenzb änder um die geschätzte Expektilfunktion. Wir entwickeln einen funktionalen Datenanalyseansatz um eine Familie von generalisierten Quantilregressionen gemeinsam zu schätzen. Dabei gehen wir in unserem Ansatz davon aus, dass die generalisierten Quantile einige gemeinsame Merkmale teilen, welche durch eine geringe Anzahl von Hauptkomponenten zusammengefasst werden können. Die Hauptkomponenten sind als Splinefunktionen modelliert und werden durch Minimierung eines penalisierten asymmetrischen Verlustmaßes gesch¨atzt. Zur Berechnung wird ein iterativ gewichteter Kleinste-Quadrate-Algorithmus entwickelt. Während die separate Schätzung von individuell generalisierten Quantilregressionen normalerweise unter großer Variablit¨at durch fehlende Daten leidet, verbessert unser Ansatz der gemeinsamen Schätzung die Effizienz signifikant. Dies haben wir in einer Simulationsstudie demonstriert. Unsere vorgeschlagene Methode haben wir auf einen Datensatz von 150 Wetterstationen in China angewendet, um die generalisierten Quantilkurven der Volatilität der Temperatur von diesen Stationen zu erhaltenGeneralized quantile regressions, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We denote $v_n(x)$ as the kernel smoothing estimator of the expectile curves. We prove the strong uniform consistency rate of $v_{n}(x)$ under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation $\sup_{ 0 \leqslant x \leqslant 1 }|v_n(x)-v(x)|$. According to the asymptotic theory, we construct simultaneous confidence bands around the estimated expectile function. We develop a functional data analysis approach to jointly estimate a family of generalized quantile regressions. Our approach assumes that the generalized quantiles share some common features that can be summarized by a small number of principal components functions. The principal components are modeled as spline functions and are estimated by minimizing a penalized asymmetric loss measure. An iteratively reweighted least squares algorithm is developed for computation. While separate estimation of individual generalized quantile regressions usually suffers from large variability due to lack of sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations
3
Yu, Keming. « Smooth regression quantile estimation ». Thesis, Open University, 1996. http://oro.open.ac.uk/57655/.
Texte intégralRésumé :
In this thesis, attention will be mainly focused on the local linear kernel regression quantile estimation. Different estimators within this class have been proposed, developed asymptotically and applied to real applications. I include algorithmdesign and selection of smoothing parameters. Chapter 2 studies two estimators, first a single-kernel estimator based on "check function" and a bandwidth selection rule is proposed based on the asymptotic MSE of this estimator. Second a recursive double-kernel estimator which extends Fan et al's (1996) density estimator, and two algorithms are given for bandwidth selection. In Chapter 3, a comparison is carried out of local constant fitting and local linear fitting using MSEs of the estimates as a criterion. Chapter 4 gives a theoretical summary and a simulation study of local linear kernel estimation of conditional distribution function. This has a special interest in itself as well as being related to regression quantiles. In Chapter 5, a kernel-version method of LMS (Cole and Green, 1992) is considered. The method proposed, which is still a semi-parametric one, is based on a general idea of local linear kernel approach of log-likelihood model. Chapter 6 proposes a two-step method of smoothing regression quantiles called BPK. The method considered is based on the idea of combining k- NN method with Healy's et al (1988) partition rule, and correlated regression model are involved. In Chapter 7, methods of regression quantile estimation are compared for different underlying models and design densities in a simulation study. The ISE criterion of interior and boundary points is used as a basis for these comparisons. Three methods are recommended for quantile regression in practice, and they are double kernel method, LMS method and Box partition kernel method (BPK). In Chapter 8, attention is turned to a novel idea of local polynomial roughness penalty regression model, where a purely theoretical framework is considered.
4
Sanches, Nathalie C. Gimenes Miessi. « Quantile regression approaches for auctions ». Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/8146.
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The goal of this thesis is to propose a new quantile regression approach to identify and estimate the quantiles of the private value conditional distribution in ascending and rst price auctions under the Independent Private Value (IPV) paradigm. The quantile regression framework provides a exible and convenient parametrization of the private value distribution, which is not a ected by the curse of dimensionality. The rst Chapter of the thesis introduces a quantile regression methodology for ascending auctions. The Chapter focuses on revenue analysis, optimal reservation price and its associated screening level. An empirical application for the USFS timber auctions suggests an optimal reservation price policy with a probability of selling the good as low as 58% for some auctions with two bidders. The second Chapter tries to address this issue by considering a risk averse seller with a CRRA utility function. A numerical exercise based on the USFS timber auctions shows that increasing the CRRA of the sellers is su cient to give more reasonable policy recommendations and a higher probability of selling the auctioned timber lot. The third Chapter develops a quantile regression methodology for rst-price auction. The estimation method combines local polynomial, quantile regression and additive sieve methods. It is shown in addition that the new quantile regression methodology is not subject to boundary issues. The choice of smoothing parameters is also discussed.
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Jeffrey, Stephen Glenn. « Quantile regression and frontier analysis ». Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/47747/.
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In chapter 3, quantile regression is used to estimate probabilistic frontiers, i.e. frontiers based on the probability of being dominated. The results from the empirical application using an Italian hotel dataset show rejections of a parametric functional form and a location shift effect, large uncertainty of the estimates of the frontier and wide confidence intervals for the estimates of efficiency. Quantile regression is further developed to estimate thick probabilistic frontiers, i.e. frontiers based on a group of efficient firms. The empirical results show that the differences between the inefficient and efficient firms at lower quantiles of the conditional distribution function are from the coefficient (85 percent of the total effect) and the residual effects (25 percent) and at higher quantiles from the coefficient (68 percent) and the regressor effects (22 percent). The results from the Monte Carlo simulations in chapter 4 show that under the correctly assumed stochastic frontier models, the probabilistic frontiers can have the lowest bias and mean squared error of the efficiency estimates. When outliers or location-scale shift effects are included, more preference is towards the probabilistic frontiers. The nonparametric probabilistic frontiers are nearly always preferable to Data Envelopment Analysis and Free Disposable Hull. In chapter 5, a fixed effects quantile regression estimator is used to estimate a cost frontier and efficiency levels for a panel dataset of English NHS Trusts. Waiting times elasticities are estimated from -0.14 to 0.17 in the cross-sectional models and -0.008 to 0.03 in the panel models. Cost minimisation ranged from 33 to 60 days in the cross-sectional model and from 37 to 54 days in the panel model. The results show that the effects of the inputs and control variables vary depending on the efficiency of the Trusts. The efficiency estimates reveal very different conclusions depending on the model choice.
6
Chao, Shih-Kang. « Quantile regression in risk calibration ». Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17223.
Texte intégralRésumé :
Die Quantilsregression untersucht die Quantilfunktion QY |X (τ ), sodass ∀τ ∈ (0, 1), FY |X [QY |X (τ )] = τ erfu ̈llt ist, wobei FY |X die bedingte Verteilungsfunktion von Y gegeben X ist. Die Quantilsregression ermo ̈glicht eine genauere Betrachtung der bedingten Verteilung u ̈ber die bedingten Momente hinaus. Diese Technik ist in vielerlei Hinsicht nu ̈tzlich: beispielsweise fu ̈r das Risikomaß Value-at-Risk (VaR), welches nach dem Basler Akkord (2011) von allen Banken angegeben werden muss, fu ̈r ”Quantil treatment-effects” und die ”bedingte stochastische Dominanz (CSD)”, welches wirtschaftliche Konzepte zur Messung der Effektivit ̈at einer Regierungspoli- tik oder einer medizinischen Behandlung sind. Die Entwicklung eines Verfahrens zur Quantilsregression stellt jedoch eine gro ̈ßere Herausforderung dar, als die Regression zur Mitte. Allgemeine Regressionsprobleme und M-Scha ̈tzer erfordern einen versierten Umgang und es muss sich mit nicht- glatten Verlustfunktionen besch ̈aftigt werden. Kapitel 2 behandelt den Einsatz der Quantilsregression im empirischen Risikomanagement w ̈ahrend einer Finanzkrise. Kapitel 3 und 4 befassen sich mit dem Problem der h ̈oheren Dimensionalit ̈at und nichtparametrischen Techniken der Quantilsregression.Quantile regression studies the conditional quantile function QY|X(τ) on X at level τ which satisfies FY |X QY |X (τ ) = τ , where FY |X is the conditional CDF of Y given X, ∀τ ∈ (0,1). Quantile regression allows for a closer inspection of the conditional distribution beyond the conditional moments. This technique is par- ticularly useful in, for example, the Value-at-Risk (VaR) which the Basel accords (2011) require all banks to report, or the ”quantile treatment effect” and ”condi- tional stochastic dominance (CSD)” which are economic concepts in measuring the effectiveness of a government policy or a medical treatment. Given its value of applicability, to develop the technique of quantile regression is, however, more challenging than mean regression. It is necessary to be adept with general regression problems and M-estimators; additionally one needs to deal with non-smooth loss functions. In this dissertation, chapter 2 is devoted to empirical risk management during financial crises using quantile regression. Chapter 3 and 4 address the issue of high-dimensionality and the nonparametric technique of quantile regression.
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Elseidi, Mohammed. « Quantile regression-based seasonal adjustment ». Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3423191.
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Time series of different nature might be characterised by the presence of deterministic and/or stochastic seasonal patterns. By seasonality, we refer to periodic fluctuations affecting not only the mean but also the shape, the dispersion and in general the density of the variable of interest over time. Using traditional approaches for seasonal adjustment might not be efficient because they do not ensure, for instance, that the adjusted data are free from periodic behaviours in, say, higher-order moments. We introduce a seasonal adjustment method based on quantile regression that is capable of capturing different forms of deterministic and/or stochastic seasonal patterns. Given a variable of interest, by describing its seasonal behaviour over an approximation of the entire conditional distribution, we are capable of removing seasonal patterns affecting the mean and/or the variance, or seasonal patterns varying over quantiles of the conditional distribution. In the first part of this work, we provide a proposed approach to deal with the deterministic seasonal pattern cases. We provide empirical examples based on simulated and real data where we compare our proposal to least-squares approaches. The results are in favour of the proposed approach in case if the seasonal patterns change across quantiles. In the second part of this work, we improve the proposed approach flexibly to account for the essential effect of the structural breaks in the time series. Again, we compare the proposed methods to segmented-least squares and provide several empirical examples based on simulated and real data that are affected by both the structural breaks and seasonal patterns. The results, in case of stochastic periodic behaviour, are in favour of the proposed approaches especially when the seasonal patterns change across quantiles.
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Liu, Xi. « Some new developments for quantile regression ». Thesis, Brunel University, 2018. http://bura.brunel.ac.uk/handle/2438/16204.
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Quantile regression (QR) (Koenker and Bassett, 1978), as a comprehensive extension to standard mean regression, has been steadily promoted from both theoretical and applied aspects. Bayesian quantile regression (BQR), which deals with unknown parameter estimation and model uncertainty, is a newly proposed tool of QR. This thesis aims to make some novel contributions to the following three issues related to QR. First, whereas QR for continuous responses has received much attention in literatures, QR for discrete responses has received far less attention. Second, conventional QR methods often show that QR curves crossing lead to invalid distributions for the response. In particular, given a set of covariates, it may turn out, for example, that the predicted 95th percentile of the response is smaller than the 90th percentile for some values of the covariates. Third, mean-based clustering methods are widely developed, but need improvements to deal with clustering extreme-type, heavy tailed-type or outliers problems. This thesis focuses on methods developed over these three challenges: modelling quantile regression with discrete responses, ensuring non-crossing quantile curves for any given sample and modelling tails for collinear data with outliers. The main contributions are listed as below: * The first challenge is studied in Chapter 2, in which a general method for Bayesian inference of regression models beyond the mean with discrete responses is developed. In particular, this method is developed for both Bayesian quantile regression and Bayesian expectile regression. This method provides a direct Bayesian approach to these regression models with a simple and intuitive interpretation of the regression results. The posterior distribution under this approach is shown to not only be coherent to the response variable, irrespective of its true distribution, but also proper in relation to improper priors for unknown model parameters. * Chapter 3 investigates a new kernel-weighted likelihood smoothing quantile regression method. The likelihood is based on a normal scale-mixture representation of an asymmetric Laplace distribution (ALD). This approach benefits of the same good design adaptation just as the local quantile regression (Spokoiny et al., 2014) does and ensures non-crossing quantile curves for any given sample. * In Chapter 4, we introduce an asymmetric Laplace distribution to model the response variable using profile regression, a Bayesian non-parametric model for clustering responses and covariates simultaneously. This development allows us to model more accurately for clusters which are asymmetric and predict more accurately for extreme values of the response variable and/or outliers. In addition to the three major aforementioned challenges, this thesis also addresses other important issues such as smoothing extreme quantile curves and avoiding insensitive to heteroscedastic errors as well as outliers in the response variable. The performances of all the three developments are evaluated via both simulation studies and real data analysis.
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Kecojevic, Tatjana. « Bootstrap inference for parametric quantile regression ». Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/bootstrap-inference-for-parametric-quantile-regression(194021d5-e03f-4f48-bfb8-5156819f5900).html.
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The motivation for this thesis came from the provision of a large data set from Saudi Arabia giving anthropometric measurements of children and adolescents from birth to eighteen years of age, with a requirement to construct growth charts. The construction of these growth charts revealed a number of issues particularly in the respect to statistical inference relating to quantile regression. To investigate a range of different statistical inference procedures in parametric quantile regression in particular the estimation of the confidence limits of the ?th (?? [0, 1]) quantile, a number of sets of simulated data in which various error structures are imposed including homoscedastic and heteroscedastic structures were developed. Methods from the statistical literature were then compared with a method proposed within this thesis based on the idea of Silverman's (1986) kernel smoothing. This proposed bootstrapping method requires the estimation of the conditional variance function of the fitted quantile. The performance of a variety of variance estimation methods combined within the proposed bootstrapping procedure are assessed under various data structures in order to examine the performance of the proposed bootstrapping approach. The validity of the proposed bootstrapping method is then illustrated using the Saudi Arabian anthropometric data.
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Waldmann, Elisabeth Anna [Verfasser]. « Bayesian Structured Additive Quantile Regression / Elisabeth Waldmann ». München : Verlag Dr. Hut, 2013. http://d-nb.info/1045126268/34.
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Aljuaid, Aziz Awadhallah S. « Bayesian quantile regression using flexible likelihood functions ». Thesis, University of Leeds, 2017. http://etheses.whiterose.ac.uk/18442/.
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Sartore, Luca. « Quantile Regression and Bass Models in Hydrology ». Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423658.
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Spatiotemporal phenomena related to the rainfall measurements can be characterised by statistical models grounded on physical concepts instead of being identified by spatiotemporal patterns based on standard correlations and related analytical tools. This perspective is useful in understanding if the relationships among neighbouring zones and consecutive years are attributable to latent physical mechanisms. Satellite data are used to examine this theory and provide evidence on empirical basis.
A recent hydrological theory, which is based on the concept of self-organisation, consists of simplified physical mechanisms that are essential for the explanation of local data relationships. The regression models inspired by the diffusion of innovation can approximate the evolution of the rainfall process within a year through a more straightforward perspective.
However, the multitude of collected data requires innovative techniques of data management and advanced analytical solutions, in order to achieve optimal results in reasonable time. Indeed, the nonlinear least squares and nonlinear quantile regression are considered to make inference on the response variable given some covariates.
A new quantile regression technique is developed in order to provide simultaneous estimates that do not violate the monotonicity property of quantiles. The nonlinear least squares highlight strong connections among rainfall and the salient features of the measurements areas. Furthermore, the quantile regression analyses quantify the intrinsic variability of the data.I fenomeni spazio-temporali relativi alle misurazioni di piovosità possono essere caratterizzati da modelli statistici fondati su concetti fisici invece di essere identificati da modelli standard basati su correlazioni spazio-temporali e i relativi strumenti analitici. Questa prospettiva è utile per capire se i rapporti tra zone confinanti e anni consecutivi sono attribuibili a meccanismi fisici latenti. Dati satellitari vengono utilizzati per esaminare questa teoria e fornire prove su base empirica. Una recente teoria idrologica, basata sul concetto di auto-organizzazione, è caratterizzata da meccanismi fisici semplificati che sono essenziali per la spiegazione delle relazioni locali presenti nei dati osservati. I modelli di regressione, che si ispirano alla teoria della diffusione di innovazioni, sono in grado di approssimare l'evoluzione del processo di precipitazione di un singolo anno attraverso una più semplice prospettiva. Tuttavia, la moltitudine di informazioni raccolte richiede tecniche innovative di gestione dei dati e soluzioni analitiche avanzate con lo scopo di ottenere risultati ottimali in tempi ragionevoli. Infatti, i minimi quadrati e la regressione quantilica per modelli non-lineari vengono utilizzati per fare inferenza sulla variabile risposta condizionatamente ad alcune covariate. Una nuova tecnica di regressione quantilica è stata sviluppata ad hoc al fine di fornire stime simultanee che non vìolino la proprietà di monotonicità dei quantili. I minimi quadrati non lineari evidenziano un forte legame tra le precipitazioni e alcune caratteristiche salienti delle zone di misurazione. Inoltre, le analisi ottenute tramite la regressione quantilica quantificano la variabilità intrinseca nei dati.
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Bonaccolto, Giovanni. « Quantile regression methods in economics and finance ». Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424494.
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In the recent years, quantile regression methods have attracted relevant interest in the statistical and econometric literature. This phenomenon is due to the advantages arising from the quantile regression approach, mainly the robustness of the results and the possibility to analyse several quantiles of a given random variable. Such as features are particularly appealing in the context of economic and financial data, where extreme events assume critical importance. The present thesis is based on quantile regression, with focus on the economic and financial environment. First of all, we propose new approaches in developing asset allocation strategies on the basis of quantile regression and regularization techniques. It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to optimize different risk and performance indicators. In particular, we introduce a risk-adjusted profitability measure, useful in evaluating financial portfolios under a pessimistic perspective, since the reward contribution is net of the most favorable outcomes. Moreover, as we consider large portfolios, we also cope with the dimensionality issue by introducing an l1-norm penalty on the assets weights. Secondly, we focus on the determinants of equity risk and their forecasting implications. Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk estimates, obtained from the Realized Range Volatility, corrected for microstructure noise and jumps, and quantile regression methods, we evaluate, in a forecasting perspective, the impact of the equity risk determinants in different volatility states and, without distributional assumptions on the realized range innovations, we recover both the points and the conditional distribution forecasts. In addition, we analyse how the relationships among the involved variables evolve over time, through a rolling window procedure. The results show evidence of the selected variables' relevant impacts and, particularly during periods of market stress, highlight heterogeneous effects across quantiles. Finally, we study the dynamic impact of uncertainty in causing and forecasting the distribution of oil returns and risk. We analyse the relevance of recently developed news-based measures of economic policy uncertainty and equity market uncertainty in causing and predicting the conditional quantiles and distribution of the crude oil variations, defined both as returns and squared returns. For this purpose, on the one hand, we study the causality relations in quantiles through a non-parametric testing method; on the other hand, we forecast the conditional distribution on the basis of the quantile regression approach and the predictive accuracy is evaluated by means of several suitable tests. Given the presence of structural breaks over time, we implement a rolling window procedure to capture the dynamic relations among the variables.Negli ultimi anni, la regressione quantile ha suscitato un notevole interesse nella letteratura statistica ed econometrica. Tale fenomeno è dovuto ai vantaggi derivanti dalla regressione quantile, in particolare, la robustezza dei risultati e la possibilità di analizzare differenti quantili di una certa variabile casuale. Tali caratteristiche sono particolarmente rilevanti nel contesto di dati economici e finanziari, data la cruciale rilevanza di eventi estremi. Innanzitutto, la tesi introduce approcci innovativi per la definizione di strategie di "asset allocation" sulla base di modelli di regressione quantile penalizzati. Come noto in letteratura, la regressione quantile minimizza il rischio estremo di portafoglio, nel momento in cui ci si focalizza sulla coda sinistra della distribuzione della variabile di risposta. Nella presente tesi si dimostra che, considerando l'intera distribuzione, è possibile ottimizzare diversi indicatori di performance e di rischiosità. In particolare, si introduce una nuova misura di performance aggiustata per il rischio, utile a valutare i portafogli finanziari in ottica pessimista. Inoltre, si dimostra che l'introduzione di una "l1-norm penalty" sui pesi dei titoli implica vantaggi non indifferenti su portafogli di notevoli dimensioni. In secondo luogo, la tesi analizza i fattori determinanti del rischio sul mercato azionario, con particolare enfasi sulle loro implicazioni previsionali. Dalla combinazione delle stime di volatilità realizzata di tipo "range-based", corrette per "noise" microstrutturali e "jumps", e modelli di regressione quantile, è possibile valutare, in ottica previsionale, l'impatto dei fattori determinanti del rischio in diversi stati del mercato e, senza assunzioni sulle innovazioni dei "realized range", ottenere le previsioni sia puntuali che sull'intera distribuzione. Inoltre, l'implementazione di una procedura a finestre mobili consente di analizzare l'evoluzione nel tempo delle relazioni tra le variabili d'interesse. Infine, l'ultimo aspetto trattato dalla tesi riguarda l'impatto dinamico dell'incertezza nel causare e prevedere la distribuzione dei rendimenti e del rischio del mercato petrolifero. L'attenzione è posta sull'impatto di due indici di tipo "news-based", recentemente elaborati, che misurano l'incertezza, rispettivamente, sulla politica economica e sui mercati azionari nel causare e prevedere le dinamiche del mercato petrolifero. A tale scopo, da un lato, la tesi esplora le relazioni di causalità nei quantili utilizzando un test non parametrico; dall'altro, la distribuzione condizionata è prevista sulla base di modelli di regressione quantile. La capacità previsionale dell'approccio adottato è valutata mediante differenti test. Data la presenza di break strutturali nel tempo, una procedura a finestre mobili è utilizzata al fine di catturare le dinamiche nei modelli proposti.
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Shows, Justin Hall. « Sparse Estimation and Inference for Censored Median Regression ». NCSU, 2009. http://www.lib.ncsu.edu/theses/available/etd-05152009-143030/.
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Censored median regression models have been shown to be useful for analyzing a variety of censored survival data with the robustness property. We study sparse estimation and inference of censored median regression. The new method minimizes an inverse censoring probability weighted least absolute deviation subject to the adaptive LASSO penalty. We show that, with a proper choice of the tuning parameter, the proposed estimator has nice theoretical properties such as root-n consistency and asymptotic normality. The estimator can also identify the underlying sparse model consistently. We propose using a resampling method to estimate the variance of the proposed estimator. Furthermore, the new procedure enjoys great advantages in computation, since its entire solution path can be obtained efficiently. Also, the method can be extended to multivariate survival data, where there is a natural or artificial clustering structure. The performance of our estimator is evaluated by extensive simulations and two real data applications.
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Rhodes, Austin James. « Accelerated Life Test Modeling Using Median Rank Regression ». Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/73362.
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Accelerated life tests (ALT) are appealing to practitioners seeking to maximize information gleaned from reliability studies, while navigating resource constraints due to time and specimen costs. A popular approach to accelerated life testing is to design test regimes such that experimental specimens are exposed to variable stress levels across time. Such ALT experiments allow the practitioner to observe lifetime behavior across various stress levels and infer product life at use conditions using a greater number of failures than would otherwise be observed with a constant stress experiment. The downside to accelerated life tests, however, particularly for those that utilize non-constant stress levels across time on test, is that the corresponding lifetime models are largely dependent upon assumptions pertaining to variant stress. Although these assumptions drive inference at product use conditions, little to no statistical methods exist for assessing their validity. One popular assumption that is prevalent in both literature and practice is the cumulative exposure model which assumes that, at a given time on test, specimen life is solely driven by the integrated stress history and that current lifetime behavior is path independent of the stress trajectory. This dissertation challenges such black box ALT modeling procedures and focuses on the cumulative exposure model in particular. For a simple strep-stress accelerated life test, using two constant stress levels across time on test, we propose a four-parameter Weibull lifetime model that utilizes a threshold parameter to account for the stress transition. To circumvent regularity conditions imposed by maximum likelihood procedures, we use median rank regression to fit and assess our lifetime model. We improve the model fit using a novel incorporation of desirability functions and ultimately evaluate our proposed methods using an extensive simulation study. Finally, we provide an illustrative example to highlight the implementation of our method, comparing it to a corresponding Bayesian analysis.Ph. D.
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Bin, Muhd Noor Nik Nooruhafidzi. « Statistical modelling of ECDA data for the prioritisation of defects on buried pipelines ». Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/16392.
Texte intégralRésumé :
Buried pipelines are vulnerable to the threat of corrosion. Hence, they are normally coated with a protective coating to isolate the metal substrate from the surrounding environment with the addition of CP current being applied to the pipeline surface to halt any corrosion activity that might be taking place. With time, this barrier will deteriorate which could potentially lead to corrosion of the pipe. The External Corrosion Direct Assessment (ECDA) methodology was developed with the intention of upholding the structural integrity of pipelines. Above ground indirect inspection techniques such as the DCVG which is an essential part of an ECDA, is commonly used to determine coating defect locations and measure the defect's severity. This is followed by excavation of the identified location for further examination on the extent of pipeline damage. Any coating or corrosion defect found at this stage is repaired and remediated. The location of such excavations is determined by the measurements obtained from the DCVG examination in the form of %IR and subjective inputs from experts which bases their justification on the environment and the physical characteristics of the pipeline. Whilst this seems to be a straight forward process, the factors that comes into play which gave rise to the initial %IR is not fully understood. The lack of understanding with the additional subjective inputs from the assessors has led to unnecessary excavations being conducted which has put tremendous financial strain on pipeline operators. Additionally, the threat of undiscovered defects due to the erroneous nature of the current method has the potential to severely compromise the pipeline's safe continual operation. Accurately predicting the coating defect size (TCDA) and interpretation of the indication signal (%IR) from an ECDA is important for pipeline operators to promote safety while keeping operating cost at a minimum. Furthermore, with better estimates, the uncertainty from the DCVG indication is reduced and the decisions made on the locations of excavation is better informed. However, ensuring the accuracy of these estimates does not come without challenges. These challenges include (1) the need of proper methods for large data analysis from indirect assessment and (2) uncertainty about the probability distribution of quantities. Standard mean regression models e.g. the OLS, were used but fail to take the skewness of the distributions involved into account. The aim of this thesis is thus, to come up with statistical models to better predict TCDA and to interpret the %IR from the indirect assessment of an ECDA more precisely. The pipeline data used for the analyses is based on a recent ECDA project conducted by TWI Ltd. for the Middle Eastern Oil Company (MEOC). To address the challenges highlighted above, Quantile Regression (QR) was used to comprehensively characterise the underlying distribution of the dependent variable. This can be effective for example, when determining the different effect of contributing variables towards different sizes of TCDA (different quantiles). Another useful advantage is that the technique is robust to outliers due to its reliance on absolute errors. With the traditional mean regression, the effect of contributing variables towards other quantiles of the dependent variable is ignored. Furthermore, the OLS involves the squaring of errors which makes it less robust to outliers. Other forms of QR such as the Bayesian Quantile Regression (BQR) which has the advantage of supplementing future inspection projects with prior data and the Logistic Quantile Regression (LQR) which ensures the prediction of the dependent variable is within its specified bounds was applied to the MEOC dataset. The novelty of research lies in the approaches (methods) taken by the author in producing the models highlighted above. The summary of such novelty includes: * The use of non-linear Quantile Regression (QR) with interacting variables for TCDA prediction. * The application of a regularisation procedure (LASSO) for the generalisation of the TCDA prediction model.* The usage of the Bayesian Quantile Regression (BQR) technique to estimate the %IR and TCDA. * The use of Logistic Regression as a guideline towards the probability of excavation * And finally, the use of Logistic Quantile Regression (LQR) in ensuring the predicted values are within bounds for the prediction of the %IR and POPD. Novel findings from this thesis includes: * Some degree of relationship between the DCVG technique (%IR readings) and corrosion dimension. The results of the relationship between TCDA and POPD highlights a negative trend which further supports the idea that %IR has some relation to corrosion. * Based on the findings from Chapter 4, 5 and 6 suggests that corrosion activity rate is more prominent than the growth of TCDA at its median depth. It is therefore suggested that for this set of pipelines (those belonging to MEOC) repair of coating defects should be done before the coating defect has reached its median size. To the best of the Author's knowledge, the process of employing such approaches has never been applied before towards any ECDA data. The findings from this thesis also shed some light into the stochastic nature of the evolution of corrosion pits. This was not known before and is only made possible by the usage of the approaches highlighted above. The resulting models are also of novelty since no previous model has ever been developed based on the said methods. The contribution to knowledge from this research is therefore the greater understanding of relationship between variables stated above (TCDA, %IR and POPD). With this new knowledge, one has the potential to better prioritise location of excavation and better interpret DCVG indications. With the availability of ECDA data, it is also possible to predict the magnitude of corrosion activity by using the models developed in this thesis. Furthermore, the knowledge gained here has the potential to translate into cost saving measures for pipeline operators while ensuring safety is properly addressed.
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Tareghian, Reza. « Application of quantile regression in climate change studies ». Wiley, 2012. http://hdl.handle.net/1993/9817.
Texte intégralRésumé :
Climatic change has been observed in many locations and has been seen to have dramatic impact on a wide range of ecosystems. The traditional method to analyse trends in climatic series is regression analysis. Koenker and Bassett (1978) developed a regression-type model for estimating the functional relationship between predictor variables and any quantile in the distribution of the response variable. Quantile regression has received considerable attention in the statistical literature, but less so in the water resources literature. This study aims to apply quantile regression to problems in water resources and climate change studies. The core of the thesis is made up of three papers of which two have been published and one has been submitted. One paper presents a novel application of quantile regression to analyze the distribution of sea ice extent. Another paper investigates changes in temperature and precipitation extremes over the Canadian Prairies using quantile regression. The third paper presents a Bayesian model averaging method for variable selection adapted to quantile regression and analyzes the relationship of extreme precipitation with large-scale atmospheric variables. This last paper also develops a novel statistical downscaling model based on quantile regression. The various applications of quantile regression support the conclusion that the method is useful in climate change studies.
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Aguilar, Fargas Joan. « Prediction interval modeling using Gaussian process quantile regression ». Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/100361.
Texte intégralRésumé :
Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, Engineering Systems Division, System Design and Management Program, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 62-65).
In this thesis a methodology to construct prediction intervals for a generic black-box point forecast model is presented. The prediction intervals are learned from the forecasts of the black-box model and the actual realizations of the forecasted variable by using quantile regression on the observed prediction error distribution, the distribution of which is not assumed. An independent meta-model that runs in parallel to the original point forecast model is responsible for learning and generating the prediction intervals, thus requiring no modification to the original setup. This meta-model uses both the inputs and output of the black-box model and calculates a lower and an upper bound for each of its forecasts with the goal that a predefined percentage of future realizations are included in the interval formed by both bounds. Metrics for the performance of the meta-model are established, paying special attention to the conditional interval coverage with respect to both time and the inputs. A series of cases studies are performed to determine the capabilities of this approach and to compare it to standard practices.
by Joan Aguilar Fargas.
S.M. in Engineering and Management
19
Koutsourelis, Antonios. « Bayesian extreme quantile regression for hidden Markov models ». Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/7071.
Texte intégralRésumé :
The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.
20
RENZETTI, STEFANO. « THE WEIGHTED QUANTILE SUM REGRESSION : EXTENSIONS AND APPLICATIONS ». Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/818694.
Texte intégralRésumé :
During these last few years an increasing body of scientific evidence showed that looking at the single exposure to chemicals without considering the mixture effect can cause an underestimate of the chemical exposures risk. This poses also statistical challenges on how to manage more complex datasets. Weighted Quantile Sum (WQS) regression is a new statistical model that allows to deal with this problems. It is able to test the association of the overall environmental exposures with an outcome and to find the main actors in the association between the exposure and the dependent variable.
Through this work we showed how we adapted the model to allow to fit a WQS regression in presence of binary, multinomial and count outcomes. Moreover, we implemented two more extensions: the possibility to test for an interaction between the WQS index (representing the overall exposure) and a continuous or categorical variable; and the ability of having two indices in the same model, one looking in the positive and the second in the negative direction when the mixture can have a bidirectional effect on the outcome. The first extension answers to a frequent and important line of inquiry in epidemiologic studies that is whether there is an effect modification (i.e., an interaction) between an exposure and a particular covariate of interest that can affect the association between the exposure and the outcome. The second extension allows to estimate both the protective and harmful effect of the mixture within the same regression model. Lastly, we showed how to apply this novel method in the genetic context thanks to the inclusion of the double WQS index. We then compared its results with the standard methodology used to test the effect of a gene set on a particular phenotype.
The simulation studies performed to test the new extensions showed the good performance of the methods reducing the bias and standard error of the estimates of the effect of the mixture on the outcome and correctly identifying the elements in the mixture that play a major role in the studied association. A high specificity was also observed. Through the case studies we were able to see how WQS confirmed previous major findings and providing new insights respect to previous literature. When we tested for the interaction between age or sex and the exposure to lead (Pb), cadmium (Cd), mercury (Hg), selenium (Se) and manganese (Mn) we found that the association between the forced vital capacity (FVC) and Pb and Hg was attenuated among older children, while female FVC is more susceptible to Cd and Hg compared to males. The application of the double index to test the association between 43 nutrients and obesity showed a harmful effect of moisture (from all sources), polyunsaturated fatty acids, saturated fatty acids, sodium, caffeine and cholesterol while a protective effect was found for beta-carotene, vitamin B12, vitamin B6, vitamin D, folic acid, vitamin C, folate DFE and alpha-carotene. Finally, through WQS we observed a significant role of the genes involved in cell-cycle in the risk of death for ovarian cancer which was not shown applying single sample Gene Set Enrichment Analysis.
The advantages of WQS regression and the extension that we described in this work are the ease of use and interpretation of the results; moreover, none of the other environmental mixture methods allow to consider the effect modification due to a covariate or to measure the amount of positive and negative association when the elements in the mixture show both effects. This work will be the starting point for additional future extensions, improvements and applications of the model while all these extensions will be implemented in the gWQS package of the statistical software R.
21
Ratnasingam, Suthakaran. « Sequential Change-point Detection in Linear Regression and Linear Quantile Regression Models Under High Dimensionality ». Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu159050606401363.
Texte intégral
22
Taylor, James William. « Predictive distributions, quantile regression and the combination of forecasts ». Thesis, London Business School (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338470.
Texte intégral
23
Al-Hamzawi, Rahim Jabbar Thaher. « Prior elicitation and variable selection for bayesian quantile regression ». Thesis, Brunel University, 2013. http://bura.brunel.ac.uk/handle/2438/7501.
Texte intégralRésumé :
Bayesian subset selection suffers from three important difficulties: assigning priors over model space, assigning priors to all components of the regression coefficients vector given a specific model and Bayesian computational efficiency (Chen et al., 1999). These difficulties become more challenging in Bayesian quantile regression framework when one is interested in assigning priors that depend on different quantile levels. The objective of Bayesian quantile regression (BQR), which is a newly proposed tool, is to deal with unknown parameters and model uncertainty in quantile regression (QR). However, Bayesian subset selection in quantile regression models is usually a difficult issue due to the computational challenges and nonavailability of conjugate prior distributions that are dependent on the quantile level. These challenges are rarely addressed via either penalised likelihood function or stochastic search variable selection (SSVS). These methods typically use symmetric prior distributions for regression coefficients, such as the Gaussian and Laplace, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression coefficients should depend on quantiles. This thesis focuses on three challenges: assigning standard quantile dependent prior distributions for the regression coefficients, assigning suitable quantile dependent priors over model space and achieving computational efficiency. The first of these challenges is studied in Chapter 2 in which a quantile dependent prior elicitation scheme is developed. In particular, an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. The prior is generalised in Chapter 3 by introducing a ridge parameter to address important challenges that may arise in some applications, such as multicollinearity and overfitting problems. The proposed prior is also used in Chapter 4 for subset selection of the fixed and random coefficients in a linear mixedeffects QR model. In Chapter 5 we specify normal-exponential prior distributions for the regression coefficients which can provide adaptive shrinkage and represent an alternative model to the Bayesian Lasso quantile regression model. For the second challenge, we assign a quantile dependent prior over model space in Chapter 2. The prior is based on the percentage bend correlation which depends on the quantile level. This prior is novel and is used in Bayesian regression for the first time. For the third challenge of computational efficiency, Gibbs samplers are derived and setup to facilitate the computation of the proposed methods. In addition to the three major aforementioned challenges this thesis also addresses other important issues such as the regularisation in quantile regression and selecting both random and fixed effects in mixed quantile regression models.
24
Reed, Craig. « Bayesian parameter estimation and variable selection for quantile regression ». Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/6118.
Texte intégralRésumé :
The principal goal of this work is to provide efficient algorithms for implementing the Bayesian approach to quantile regression. There are two major obstacles to overcome in order to achieve this. Firstly, it is necessary to specify a suitable likelihood given that the frequentist approach generally avoids such speci cations. Secondly, sampling methods are usually required as analytical expressions for posterior summaries are generally unavailable in closed form regardless of the prior used. The asymmetric Laplace (AL) likelihood is a popular choice and has a direct link to the frequentist procedure of minimising a weighted absolute value loss function that is known to yield the conditional quantile estimates. For any given prior, the Metropolis Hastings algorithm is always available to sample the posterior distribution. However, it requires the speci cation of a suitable proposal density, limiting it's potential to be used more widely in applications. It is shown that the Bayesian quantile regression model with the AL likelihood can be converted into a normal regression model conditional on latent parameters. This makes it possible to use a Gibbs sampler on the augmented parameter space and thus avoids the need to choose proposal densities. Using this approach of introducing latent variables allows more complex Bayesian quantile regression models to be treated in much the same way. This is illustrated with examples varying from using robust priors and non parametric regression using splines to allowing model uncertainty in parameter estimation. This work is applied to comparing various measures of smoking and which measure is most suited to predicting low birthweight infants. This thesis also offers a short tutorial on the R functions that are used to produce the analysis.
25
Noufaily, Angela. « Parametric quantile regression based on the generalised gamma distribution ». Thesis, Open University, 2011. http://oro.open.ac.uk/54496/.
Texte intégralRésumé :
Quantile regression offers an extension to regression analysis where a modified version of the least squares method allows the fitting of quantiles at every percentile of the data rather than the mean only. Using the well-known three-parameter generalised gamma distribution to model variation in data, we present a parametric quantile regression study for positive univariate reference charts. The study constitutes an overall package that includes all different stages of parametric modeling starting from model identification to parameter estimation, model selection and finally model checking. We improve on earlier work by being the first to formulate the iterative approach to solution of the likelihood score equations of the generalised gamma distribution in such a way that the individual equations involved are uniquely solvable and far from being problematic as a number of authors have suggested. We conduct likelihood ratio tests to choose the best model within the three-, four-, five- and six-parameter generalised gamma family obtained by making the parameters linearly (or loglinearly) dependent on a univariate covariate. Quantiles are plotted accordingly and asymptotic theory for obtaining the expressions for confidence bands around them is given. Based on the chi-square goodness-of-fit test, we suggest a test statistic that checks the goodness of the generalised gamma model for given data. We validate the whole theoretical process computationally via simulations. Lastly, we demonstrate the different steps of the proposed modeling procedure through two main applications; one is environment-related and the other health-related. In a parallel fashion, inspired by the generalised gamma distribution, we introduce an alternative three-parameter distribution with useful statistical properties. We explore briefly maximum likelihood estimation and asymptotic theory of the alternative distribution and we compare it computationally to the generalised gamma.
26
DE, PAOLA ROSITA. « Median estimation using auxiliary variables ». Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/36075.
Texte intégralRésumé :
In the present study the estimation of the median has been taken into consideration
using different methods of analysis.
First of all the estimation of the median without auxiliary information is analyzed.
Then the method of Kuk and Mak proposed in 1989 is exposed: this way
of estimating the median is based on the knowledge of the population median of
auxiliary variable X. Another method, which considers the median of the auxiliary
variable is the ratio estimator. Then two methods based on the regression
estimator are analyzed : the first one considers the regression based on the median
regression, the second one is based on the minimum square method.
Two experiments have been carried out in order to compare the methods proposed.
First of all the methods are compared selecting all possible samples from
nine di_erent small populations.
The second application is based on the selection of couples of random numbers
from a bivariate random variable distributed as a Bivariate Log-Normal distribution.
Also in this situation the methods of estimation of the median are compared
considering the expected values and mean square errors.
27
Guo, Mengmeng Verfasser], Wolfgang [Akademischer Betreuer] [Härdle et Jianhua [Akademischer Betreuer] Huang. « Generalized quantile regression / Mengmeng Guo. Gutachter : Wolfgang Härdle ; Jianhua Huang ». Berlin : Humboldt Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2012. http://d-nb.info/1025501047/34.
Texte intégral
28
Huang, Shui-mei, et 黃秀梅. « quantile regression ». Thesis, 2006. http://ndltd.ncl.edu.tw/handle/59580896304481039057.
Texte intégral
29
Lo, Yi, et 羅驛. « Weighted Quantile Regression ». Thesis, 2010. http://ndltd.ncl.edu.tw/handle/31421059248782021412.
Texte intégral
30
Reich, BJ, M. Fuentes et DB Dunson. « Bayesian Spatial Quantile Regression ». Thesis, 2011. http://hdl.handle.net/10161/2981.
Texte intégralRésumé :
Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this paper we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We develop a spatial quantile regression model that does not assume normality and allows the covariates to affect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior. For extremely large datasets our model is computationally infeasible, and we develop an approximate method. We apply the approximate version of our model to summer ozone from 1997-2005 in the Eastern U.S., and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors fixed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast.Dissertation
31
Lamarche, Carlos Eduardo. « Quantile regression for panel data / ». 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3242908.
Texte intégralRésumé :
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.Source: Dissertation Abstracts International, Volume: 67-11, Section: A, page: 4289. Adviser: Roger Koenker. Includes bibliographical references (leaves 134-138) Available on microfilm from Pro Quest Information and Learning.
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« Robust Quantile Regression Using L2E ». Thesis, 2012. http://hdl.handle.net/1911/70304.
Texte intégralRésumé :
Quantile regression, a method used to estimate conditional quantiles of a set of data ( X, Y ), was popularized by Koenker and Bassett (1978). For a particular quantile q , the q th quantile estimate of Y given X = x can be found using an asymmetrically-weighted, absolute-loss criteria. This form of regression is considered to be robust, in that it is less affected by outliers in the data set than least-squares regression. However, like standard L 1 regression, this form of quantile regression can still be affected by multiple outliers. In this thesis, we propose a method for improving robustness in quantile regression through an application of Scott's L 2 Estimation (2001). Theoretic and asymptotic results are presented and used to estimate properties of our method. Along with simple linear regression, semiparametric extensions are examined. To verify our method and its extensions, simulated results are considered. Real data sets are also considered, including estimating the effect of various factors on the conditional quantiles of child birth weight, using semiparametric quantile regression to analyze the relationship between age and personal income, and assessing the value distributions of Major League Baseball players.
33
吳國傑. « Penalized Estimation for Quantile Regression ». Thesis, 2011. http://ndltd.ncl.edu.tw/handle/09966629602473364803.
Texte intégralRésumé :
碩士國立清華大學
統計學研究所
99
Quantile regression (QR) describes the relationship between the response variable and the exploratory variables through some specific quantiles, which has been applied to a wide range of data and different fields. Under the linear model assumption, Zou and Yuan (2008) proposed the composite quantile regression (CQR) to incorporate several quantiles at a time in the estimation function. In theory, CQR has better estimation precision when the linear model assumption holds, but it is not adequate and biased when the assumption is wrong. Without the linear model assumption, this thesis suggest a penalized quantile regression (PQR) method which implements either QR or CQR according to the empirical data property, by including a specific grouped lasso regularization term on the regression parameters in the estimation function. Simulation results show that PQR has good estimation performance over the QR and CQR under various situations.
34
Yan, Yin-Jhen, et 顏吟真. « Geographically Weighted Autoregressive Quantile Regression ». Thesis, 2012. http://ndltd.ncl.edu.tw/handle/23202505988854401388.
Texte intégralRésumé :
碩士淡江大學
統計學系碩士班
100
Geographically Weighted Regression (GWR; Brunsdon et al., 1998) and Quantile Regression (QR; Koenker and Bassett, 1978) are two important tools respectively in geography and econometrics in analyzing various issues of empirical studies. The former is designed to explore spatial nonstationarity and the latter is constructed to model relationships among variables across the whole distribution of a dependent variable. While both of these methods have been widely used in literature, they seem to be two unconnected lines of knowledge inquiry until recently (Chen et al., 2012). Chen et al. developed an approach so-called GeographicallyWeighted Quantile Regression (GWQR) to integrate QR and GWR. This innovative approach can explore the spatial nonstationarity not only over space but also across different levels of the dependent variable. It is, however, argued as a methodological issue that the GWQR does not account for spatial dependence between geographic locations. The goal of this study is then to address such perceived gap, and to introduce a Geographically Weighted Autoregressive Quantile Regression (GWAQR) model which includes (local) spatial lag autocorrelation components. A simulation study is conducted as well to examine the performance of the proposed estimator and further validate the GWAQR methodology.
35
Tai, Yun Chiang, et 戴允強. « New Algorithms for Monotone Nonparametric Regression and Monotone Quantile Regression ». Thesis, 2000. http://ndltd.ncl.edu.tw/handle/57201176596846154809.
Texte intégralRésumé :
碩士國立交通大學
統計所
88
A monotone nonparametric regression model is considered and a constrained weighted least squares solution is proposed for estimating monotone smooth functions from noisy data.The estimate obtained guarantees the monotonicity requirement.An efficient algorithm for computing the proposed solution is developed based on Lemke's algorithm for solving linear complemetarity problems.The leave-one-out cross validation method was adopted for the bandwidth selection.In addition,we propose a monotone nonparametric quantile regression method for interval estimation of the mean function.An iterative algorithm is developed for computing the quantile estimates.The proposed methods are demonstrated by some simulated numerical examples and a real example.The results indicate that the proposed methods are quite promising.
36
Chiang, Chih-Lun, et 姜智倫. « Decomposition of Gender Discrimination : Quantile Regression ». Thesis, 2008. http://ndltd.ncl.edu.tw/handle/62ey25.
Texte intégralRésumé :
碩士國立暨南國際大學
經濟學系
96
This research simultaneously uses the quantile regression model which is recently developed and the traditional mean regression model to estimate the male and female wage function. And penetrating the different models of decomposition of gender difference, discusses the marginal return difference, the discrimination degree change and the cross time tendency of men and women employed under the different wage level in Taiwan. Aside from the well-developed ordinary least square analyze in the existing literature. Three conclusions are found in this paper. First, the male’s wage level generally is higher than the female’s and the wages difference discriminates occupies the majority. Second, the sex discrimination degree approximately drops along with the wage level enhancement. Third, the wage gap between male and female is reducing in recent years, but the female received the discrimination degree is actually rising. This phenomenon deserves further consideration for future policy suggestion.
37
Wong, Jia-Cong, et 翁嘉聰. « Bayesian Asymmetric Causality in Quantile Regression ». Thesis, 2009. http://ndltd.ncl.edu.tw/handle/49345125503369074425.
Texte intégralRésumé :
碩士逢甲大學
統計與精算所
97
The purpose of this thesis is to propose a nonlinear Granger-causality test over a range of quantile levels in financial market. We consider quantile regression with heteroskedastic errors to discuss causal relation between futures and stock returns, while the traditional regression model cannot fully obtain the behavior of extreme values. To investigate the linkage for international stock markets, the proposed causality test includes three features: asymmetry, heteroskedasticity and quantile causal effect. We use Bayesian Markov chain Monte Carlo methods to investigate the asymmetric causal effects between futures and stock returns. The results of simulation study show that the parameters are reasonably estimated at all quantile levels, especially for capturing the spillover effect of an exogenous variable. In empirical applications, we examine dynamic linkages among two future markets and one stock market, namely Morgan Stanley Capital International (MSCI) Taiwan stock index futures of Singapore International Monetary Exchange (SIMEX), Taiwan stock index futures market of Taiwan Futures Exchange (TAIFEX) and Taiwan stock returns. There is a significant bi-directional causality between MSCI Taiwan stock index futures of SIMEX and Taiwan stock index futures market returns of TAIFEX at low quantile levels. Furthermore, we consider the Granger-Causal effects of two futures corresponding to the Taiwan stock returns. There are significant Granger-causal effects with considered models at the extreme quantile levels.Finally, we employ the DIC measure to select useful threshold models.
38
Chang, Ting-Wei, et 張庭威. « Gibrat''s Law：Application of Quantile Regression ». Thesis, 2004. http://ndltd.ncl.edu.tw/handle/11358072765132021735.
Texte intégralRésumé :
碩士淡江大學
產業經濟學系碩士班
94
Gibrat’s Law indicates that the growth rate of a given firm is independent of its size. In the literature, both supporting and opposing opinions coexist. Scholars investigating firms exceeding the minimum scale tended to agree with Gibrat’s Law; for example, Hart and Prais (1956). In contrast, scholars investigating small firms tended to disagree with Gibrat’s Law; for example, Dunne and Hughes (1994). Recently, Lotti et al. (2003) analyzed the data of Italian manufacturing firms over the period from 1987 to 1993 and used quantile regression techniques to test whether Gibrat’s Law holds for new small firms in the early stage of their life cycle. Their main finding is that small firms have to rush in order to achieve a size large enough to enhance their likelihood of survival. Conversely, in subsequent years the patterns of growth rate of new smaller firms do to differ significantly from those of relatively larger entrants, and the Law cannot be rejected. This thesis applied the method of quantile regression and analyzed the data of DTI-Meeks-Whittington British firms over the period from 1955 to 1985. It aimed at using relatively older and larger firms’ data to compare with Lotti’s results and to compare the results from quantile regression with the results from the conventional method, OLS, which was used to investigate firms exceeding MES. In contrast to the results of Lotti et al. (2003), the results of this thesis indicate that Gibrat’s Law only holds at low-quantile and being rejected at other quantiles. In particular, the high-quantile in large firms tends to reject Gibrat’s Law. This finding is also different from the results of Hart and Prais (1956), which supported the Law while investigating firms exceeding MES.
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Wang, Chu-Chun, et 王筑羣. « Test of CAPM by Quantile Regression ». Thesis, 2004. http://ndltd.ncl.edu.tw/handle/46159136613787070441.
Texte intégralRésumé :
碩士淡江大學
財務金融學系碩士班
94
This paper proposes that if we consider the real circumstance of market which may not be the high risky high return and the assumed model is under the non-linear state, how we can do the analysis and measurement for the CAPM? We select the monthly data from July of 1926 to August of 2005, and try to use the model of Fama and MacBeth (1973) as the basis in this text. We also use the method of Quantile Regression to discuss the relationship between the market risk of investment portfolio and the rate of return, in addition, we can identify the assumption of the perfect linear model is whether or not correct. Furthermore, we also can analyze the behavior of the model under different quantiles, and then understand the possibility of practical applications in CAPM. From the result of this research, under the lower degree of the quantile level, the assumption of the positive slope of CAPM and the result of the traditional least square method are contradictive, that is, the relationship between systematic risk and the rate of portfolio returns are not be the positive correlation permanently. Moreover, under the situation of not set the parameter of model and use the nonparametric method to calculate and estimate, the result is also present a contradiction to the linear assumption of CAPM, that is, using the method of quantile regression to make a demonstration that the two assumptions of CAPM which are positive slop and perfect linear are not always correct.
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Ayilara, Olawale Fatai. « Quantile regression with rank-based samples ». 2016. http://hdl.handle.net/1993/31918.
Texte intégralRésumé :
Quantile Regression, as introduced by Koenker, R. and Bassett, G. (1978), provides
a complete picture of the relationship between the response variable and covariates
by estimating a family of conditional quantile functions. Also, it offers a natural
solution to challenges such as; homoscedasticity and sometimes unrealistic normality
assumption in the usual conditional mean regression. Most of the results for quantile
regression are based on simple random sampling (SRS). In this thesis, we study
the quantile regression with rank-based sampling methods. Rank-based sampling
methods have a wide range of applications in medical, ecological and environmental
research, and have been shown to perform better than SRS in estimating several
population parameters. We propose a new objective function which takes into
account the ranking information to estimate the unknown model parameters based
on the maxima or minima nomination sampling designs. We compare the mean
squared error of the proposed quantile regression estimates using maxima (or minima)
nomination sampling design and observe that it provides higher relative e ciency
when compared with its counterparts under SRS design for analyzing the upper
(or lower) tails of the distribution of the response variable. We also evaluate the
performance of our proposed methods when ranking is done with error.February 2017
41
吳晉輝. « Quantile Regression for Censored Cost Data ». Thesis, 2018. http://ndltd.ncl.edu.tw/handle/7e95q9.
Texte intégralRésumé :
碩士國立嘉義大學
農藝學系研究所
106
Because cost responses are generally skewed to the right, this paper proposes to model the quantile of cost to handle covariate information. Cost data usually have the problem of induced informative censoring when some subjects are not traced until the endpoint of study so that their total costs are observed incompletely. Due to induced informative censoring, we use an inverse probability of censoring weighted (IPCW) estimating equation to obtain regression coefficients under the quantile model. The perturbation resampling method is employed to estimate the standard errors. We evaluate the finite-sample performance of the proposed methodology via extensive simulation studies.
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LIN, TZU-LING, et 林姿伶. « Insurance and Economic Growth : Quantile Regression ». Thesis, 2018. http://ndltd.ncl.edu.tw/handle/zhqa6a.
Texte intégralRésumé :
博士逢甲大學
金融博士學位學程
106
This study examines the long-run equilibrium and short-term causality between insurance market development and economic growth. The study group includes the seven major industrial countries (Group of 7, G7). The sample period is from 1980 to 2014. The study divides the development of the insurance market into life insurance, property insurance, and total insurance. It examines insurance density, insurance penetration and insurance premium income in Direct US Dollars. This study not only considers the long-term relationship between insurance demand and gross domestic product (GDP) but also focuses on short-term cause-and-effect relationships. It also discusses two competing hypotheses: supply-leading and demand-following. As regards long-term relationships, the traditional two-stage cointegration test and quantiles cointegration test are used to test the long-term cointegration relationship between variables to verify whether there is a long-term equilibrium relationship between the insurance market development and the overall economic growth. The study shows that there is a cointegration relationship between insurance development and gross domestic product, which means that there is a long-term equilibrium relationship between insurance development and economic growth. For short-term causality, the Granger causality test and the regression test are used to verify the short-term causal relationship between insurance demand and economic growth. The study found that short-term causality shows that short-term dynamic adjustments take on multiple forms, include one-way, two-way and independence and other directions of causality. Insurance plays a very important role in the financial research field, but it is often overlooked on financial development and economic growth in the literature. This study break through previous research methods and uses a quantiles regression model to analyze the relationship between economic growth and insurance development to make up the insufficiency for previous literature on insurance-related activities.
43
Chu, Wei-Chieh, et 朱韋杰. « Panel Data Quantile Regression with Endogeneity ». Thesis, 2018. http://ndltd.ncl.edu.tw/handle/84hjd7.
Texte intégral
44
Ling, Wodan. « Quantile regression for zero-inflated outcomes ». Thesis, 2019. https://doi.org/10.7916/d8-rre7-sw52.
Texte intégralRésumé :
Zero-inflated outcomes are common in biomedical studies, where the excessive zeros indicate some special but undetectable events. Quantile regression is potentially advantageous in analyzing zero-inflated outcomes due to two reasons. First, compared to parametric models such as the zero-inflated Poisson and two-part model, quantile regression gives robust and accurate estimation by avoiding likelihood specification and can capture the tail events and heterogeneity over the outcome distribution. Second, while the mean-based regression may be misinterpreted for a zero-inflated outcome, the interpretation of quantiles is naturally compatible with the underlying process that such an outcome intends to measure. Unfortunately, uncorrected linear quantile regression is not directly applicable because of two reasons. First, the feasibility of estimation and validity of inference of quantile regression require the conditional distribution of outcomes to be absolutely continuous, which is violated due to zero-inflation. Second, direct quantile regression implicitly assumes a constant chance to observe a positive outcome, but the degree of zero-inflation varies with the covariates in most cases. Thus the conditional quantile function of the outcome depends on the covariates in a nonlinear fashion. To analyze the zero-inflated outcomes by taking advantage of the merits of quantile regression, we propose a novel quantile regression framework that can address all the issues above.
In the first part of this dissertation, we propose a two-part model that comprises a logistic regression for the probability of being positive, and a linear quantile regression for the positive part with subject-specific zero-inflation adjusted. Inference on the estimated conditional quantile and covariate effect are not trivial based on such a two-part model. We then develop an algorithm to achieve a consistent estimation of the conditional quantiles, while circumventing the unbounded variance at the quantile level where the conditional quantile changes from zero to positive. Furthermore, we develop an inference tool to determine the quantile treatment effect associated with a covariate at a given quantile level. We evaluate the proposed method and compare it with existing approaches by simulation studies and a real data analysis aimed at studying the risk factors for carotid atherosclerosis.
In the second part, based on the proposed two-part model mentioned above, we develop ZIQRank, a zero-inflated quantile rank-score based test to detect the difference in distributions. The proposed test extends the local inference in the first part to a simultaneous one. It is powerful to handle zero-inflation and heterogeneity simultaneously. It comprises a valid test of logistic regression for the zero-inflation and rank-score based tests on multiple quantiles for the positive part with zero-inflation adjusted. The p-values are combined with a procedure selected according to the extent of zero-inflation and heterogeneity of the data. Simulation studies show that compared to existing tests, the proposed test has a higher power in detecting differential distributions. Finally, we apply the ZIQRank test to a human scRNA-seq data to study differentially expressed genes in Neoplastic and Regular cells. It successfully discovers a group of crucial genes associated with glioma, while the other methods fail to do so.
In the third part, we extend the proposed two-part quantile regression model for zero-inflated outcomes and the ZIQRank test to analyze longitudinal data. Each part of the proposed two-part model is modified as a marginal longitudinal model (GEE), conditioning on the outcome at the previous time point and its zero/positive status. We apply the model and the test to study the effect of a recommender system aimed at boosting user engagement of a suite of smartphone apps designed for depressed patients. Our novel model framework demonstrates a dominating performance in model fitting, prediction, and critical feature detection, compared to the existing methods.
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SABBI, ALBERTO. « Mixed effect quantile and M-quantile regression for spatial data ». Doctoral thesis, 2020. http://hdl.handle.net/11573/1456341.
Texte intégralRésumé :
Observed data are frequently characterized by a spatial dependence; that is the observed values can be influenced by the "geographical" position. In such a context it is possible to assume that the values observed in a given area are similar to those recorded in neighboring areas. Such data is frequently referred to as spatial data and they are frequently met in epidemiological, environmental and social studies, for a discussion see Haining, (1990). Spatial data can be multilevel, with samples being composed of lower level units (population, buildings) nested within higher level units (census tracts, municipalities, regions) in a geographical area.
Green and Richardson (2002) proposed a general approach to modelling spatial data based on finite mixtures with spatial constraints, where the prior probabilities are modelled through a Markov Random Field (MRF) via a Potts representation (Kindermann and Snell, 1999, Strauss, 1977). This model was defined in a Bayesian context, assuming that the interaction parameter for the Potts model is fixed over the entire analyzed region. Geman and Geman (1984) have shown that this class process can be modelled by a Markov Random Field (MRF). As proved by the Hammersley-Clifford theorem, modelling the process through a MRF is equivalent to using a Gibbs distribution for the membership vector. In other words, the spatial dependence between component indicators is captured by a Gibbs distribution, using a representation similar to the Potts model discussed by Strauss (1977).
In this work, a Gibbs distribution, with a component specific intercept and a constant interaction parameter, as in Green and Richardson (2002), is proposed to model effect of neighboring areas.
This formulation allows to have a parameter specific to each component and a constant spatial dependence in the whole area, extending to quantile and m-quantile regression the proposed by Alfò et al. (2009) who suggested to have both intercept and interaction parameters depending on the mixture component, allowing for different prior probability and varying strength of spatial dependence.
We propose, in the current dissertation to adopt this prior distribution to define a Finite mixture of quantile regression model (FMQRSP) and a Finite mixture of M-quantile regression model (FMMQSP), for spatial data.
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Tsai, Min-Jen, et 蔡敏仁. « Internationalization and Wage Inequality : Quantile Regression Analysis ». Thesis, 2008. http://ndltd.ncl.edu.tw/handle/x42sza.
Texte intégralRésumé :
碩士國立暨南國際大學
經濟學系
96
The purpose of this study is to estimate skilled and unskilled male wage inequality of Taiwanese manufacturing focusing on globalization covariates, foreign trade and outward direct investment in particular, from 1989 to 2006. Quantile regression model and traditional ordinary least square regression model are used to address the issues with the combined data from Manpower Utilization Survey, Trade Data and Outward Investment Data in Taiwan. The empirical findings suggest that the effect of internationalization on wage inequality varies across different development stages of Taiwan and that of trade partners. In consequence, result of trade and direct investment on wage inequality is inconsistent with the prediction of the traditional Heckscher-Ohlin-Samuelson theory. Possible explanation is that market integration and technology learning make the results deviate from traditional theory. Besides, it’s found that outward direct investment plays a crucial role in wage equation. Thus, examining wage inequality within internationalization fracework should not ignore the possible effect of outward direct investment. In sum, direct investment and foreign trade in addition to the traditional human capital variables are important determinants in wages structure over the development process of internationalization.
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Wang, Yini. « Three Essays on Time Series Quantile Regression ». Thesis, 2012. http://hdl.handle.net/1974/7340.
Texte intégralRésumé :
This dissertation considers quantile regression models with nonstationary or nearly nonstationary time series. The first chapter outlines the thesis and discusses its theoretical and empirical contributions. The second chapter studies inference in quantile regressions with cointegrated variables allowing for multiple structural changes. The unknown break dates and regression coefficients are estimated jointly and consistently. The conditional quantile estimator has a nonstandard limit distribution. A fully modified estimator is proposed to remove the second-order bias and nuisance parameters and the resulting limit distribution is mixed normal. A simulation study shows that the fully modified quantile estimator has good finite sample properties. The model is applied to stock index data from the emerging markets of China and several mature markets. Financial market integration is found in some quantiles of the Chinese stock indices. The third chapter considers predictive quantile regression with a nearly integrated regressor. We derive nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes. The critical values are found to depend on both the quantile of interest and the local-to-unity parameter, which is not consistently estimable. Based on these critical values, we propose a valid Bonferroni bounds test for quantile predictability with persistent regressors. We employ this new methodology to test the ability of many commonly employed and highly persistent regressors, such as the dividend yield, earnings price ratio, and T-bill rate, to predict the median, shoulders, and tails of the stock return distribution. Chapter Four proposes a cumulated sum (CUSUM) test for the null hypothesis of quantile cointegration. A fully modified quantile estimator is adopted for serial correlation and endogeneity corrections. The CUSUM statistic is composed of the partial sums of the residuals from the fully modified quantile regression. Under the null, the test statistic converges to a functional of Brownian motions. In the application to U.S. interest rates of different maturities, evidence in favor of the expectations hypothesis for the term structure is found in the central part of the distributions of the Treasury bill rate and financial commercial paper rate, but in the tails of the constant maturity rate distribution.Thesis (Ph.D, Economics) -- Queen's University, 2012-07-30 15:20:38.253
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« Weighted quantile regression and oracle model selection ». Thesis, 2009. http://library.cuhk.edu.hk/record=b6074984.
Texte intégralRésumé :
In this dissertation I suggest a new (regularized) weighted quantile regression estimation approach for nonlinear regression models and double threshold ARCH (DTARCH) models. I allow the number of parameters in the nonlinear regression models to be fixed or diverge. The proposed estimation method is robust and efficient and is applicable to other models. I use the adaptive-LASSO and SCAD regularization to select parameters in the nonlinear regression models. I simultaneously estimate the AR and ARCH parameters in the DTARCH model using the proposed weighted quantile regression. The values of the proposed methodology are revealed.Keywords: Weighted quantile regression, Adaptive-LASSO, High dimensionality, Model selection, Oracle property, SCAD, DTARCH models.
Under regularity conditions, I establish asymptotic distributions of the proposed estimators, which show that the model selection methods perform as well as if the correct submodels are known in advance. I also suggest an algorithm for fast implementation of the proposed methodology. Simulations are conducted to compare different estimators, and a real example is used to illustrate their performance.
Jiang, Xuejun.
Adviser: Xinyuan Song.
Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: .
Thesis (Ph.D.)--Chinese University of Hong Kong, 2009.
Includes bibliographical references (leaves 86-92).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
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« Bayesian Quantile Regression in Latent Variable Models ». 2016. http://repository.lib.cuhk.edu.hk/en/item/cuhk-1292471.
Texte intégral
50
Wang, Chih-Kai, et 王志凱. « Quantile Regression Analysis in Taiwan’s Futures Market ». Thesis, 2007. http://ndltd.ncl.edu.tw/handle/11183793410147767000.
Texte intégralRésumé :
碩士國立臺灣大學
農業推廣學研究所
95
The objective of this study is to apply quantile regression method to the relationships of return-volume and the return-foreign oil price in Taiwan’s Futures Exchange. The empirical results show that the return-volume relationships in the four futures, which are TX, MTX, TE, and TF are quite different. There are some significant positive return-volume relationships across quantiles, showing that a large positive return is usually accompanied with a large trading volume and a large negative return with a small trading volume, yet the effect of former is stronger. And the others are different from the former. However, such relations change when returns approach the price limits. For the return-foreign oil price relations, the empirical results show that the return-foreign oil price relations in four futures, which are TX, MTX, TE, and TF are almost the same. When returns approach the price limits, such effects change and become strong. On the other hand, linear regressions estimated by the ordinary least square method are unable to reveal such patterns.