Relevant bibliographies by topics / Median regression, quantile regression

Academic literature on the topic 'Median regression, quantile regression'

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Published: 9 March 2023
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Journal articles on the topic "Median regression, quantile regression"

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Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.
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Aviral, Kumar Tiwari, and Krishnankutty Raveesh. "Determinants of Capital Structure: A Quantile Regression Analysis." Studies in Business and Economics 10, no. 1 (April 1, 2015): 16–34. http://dx.doi.org/10.1515/sbe-2015-0002.

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Abstract In this study, we attempted to analyze the determinants of capital structure for Indian firms using a panel framework and to investigate whether the capital structure models derived from Western settings provide convincing explanations for capital structure decisions of the Indian firms. The investigation is performed using balanced panel data procedures for a sample 298 firms (from the BSE 500 firms based on the availability of data) during 2001-2010. We found that for lowest quantile LnSales and TANGIT are significant with positive sign and NDTS and PROFIT are significant with negative sign. However, in case of 0.25th quantile LnSales and LnTA are significant with positive sign and PROFIT is significant with negative sign. For median quantile PROFIT is found to be significant with negative sign and TANGIT is significant with positive sign. For 0.75th quantile, in model one, LnSales and PROFIT are significant with negative sign and TANGIT and GROWTHTA are significant with positive sign whereas, in model two, results of 0.75th quantile are similar to the median quantile of model two. For the highest quantile, in case of model one, results are similar to the case of 0.75th quantile with exception that now GROWTHTA in model one (and GROWTHSA in model two).
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CAI, YUZHI. "A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS." International Journal of Theoretical and Applied Finance 19, no. 03 (April 21, 2016): 1650016. http://dx.doi.org/10.1142/s0219024916500163.

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Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.
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Chiu, Yohann Moanahere, Fateh Chebana, Belkacem Abdous, Diane Bélanger, and Pierre Gosselin. "Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach." International Journal of Environmental Research and Public Health 18, no. 24 (December 16, 2021): 13277. http://dx.doi.org/10.3390/ijerph182413277.

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Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.
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UTHAMI, IDA AYU PRASETYA, I. KOMANG GDE SUKARSA, and I. PUTU EKA NILA KENCANA. "REGRESI KUANTIL MEDIAN UNTUK MENGATASI HETEROSKEDASTISITAS PADA ANALISIS REGRESI." E-Jurnal Matematika 2, no. 1 (January 30, 2013): 6. http://dx.doi.org/10.24843/mtk.2013.v02.i01.p021.

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In regression analysis, the method used to estimate the parameters is Ordinary Least Squares (OLS). The principle of OLS is to minimize the sum of squares error. If any of the assumptions were not met, the results of the OLS estimates are no longer best, linear, and unbiased estimator (BLUE). One of the assumptions that must be met is the assumption about homoscedasticity, a condition in which the variance of the error is constant (same). Violation of the assumptions about homoscedasticity is referred to heteroscedasticity. When there exists heteroscedas­ticity, other regression techniques are needed, such as median quantile regression which is done by defining the median as a solution to minimize sum of absolute error. This study intended to estimate the regression parameters of the data were known to have heteroscedasticity. The secondary data were taken from the book Basic Econometrics (Gujarati, 2004) and analyzing method were performed by EViews 6. Parameter estimation of the median quantile regression were done by estimating the regression parameters at each quantile ?th, then an estimator was chosen on the median quantile as regression coefficients estimator. The result showed heteroscedasticity problem has been solved with median quantile regression although error still does not follow normal distribution properties with a value of R2 about 71 percent. Therefore it can be concluded that median quantile regression can overcome heteroscedasticity but the data still abnormalities.
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I. O., Ajao,, Obafemi, O. S., and Osunronbi, F.A. "MEASURING THE IMPACT OF TAU VECTOR ON PARAMETER ESTIMATES IN THE PRESENCE OF HETEROSCEDASTIC DATA IN QUANTILE REGRESSION ANALYSIS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 31, 2023): 3220–29. http://dx.doi.org/10.47191/ijmcr/v11i1.15.

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The ordinary least squares (OLS) regression models only the conditional mean of the response and is computationally less expensive. Quantile regression on the other hand is more expensive and rigorous but capable of handling vectors of quantiles and outliers. Quantile regression does not assume a particular parametric distribution for the response, nor does it assume a constant variance for the response, unlike least squares regression. This paper examines the impact of various quantiles (tau vector) on the parameter estimates in the models generated by the quantile regression analysis. Two data sets, one with normal random error with non-constant variances and the other with a constant variance were simulated. It is observed that with heteroscedastic data the intercept estimate does not change much but the slopes steadily increase in the models as the quantile increase. Considering homoscedastic data, results reveal that most of the slope estimates fall within the OLS confidence interval bounds, only few quartiles are outside the upper bound of the OLS estimates. The hypothesis of quantile estimates equivalence is rejected, which shows that the OLS is not appropriate for heteroscedastic data, but the assumption is not rejected in the case of homoscedastic data at 5% level of significance, which clearly proved that the quantile regression is not necessary in a constant variance data. Using the following accuracy measures, mean absolute percentage error (MAPE), the median absolute deviation (MAD) and the mean squared deviation (MSD), the best model for the heteroscedastic data is obtained at the first quantile level (tau = 0.10).
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Conaway, Mark. "Reference data and quantile regression." Muscle & Nerve 40, no. 5 (October 13, 2009): 751–52. http://dx.doi.org/10.1002/mus.21562.

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Pan, Wen-Tsao, and Yungho Leu. "An Analysis of Bank Service Satisfaction Based on Quantile Regression and Grey Relational Analysis." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/1475148.

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Bank service satisfaction is vital to the success of a bank. In this paper, we propose to use the grey relational analysis to gauge the levels of service satisfaction of the banks. With the grey relational analysis, we compared the effects of different variables on service satisfaction. We gave ranks to the banks according to their levels of service satisfaction. We further used the quantile regression model to find the variables that affected the satisfaction of a customer at a specific quantile of satisfaction level. The result of the quantile regression analysis provided a bank manager with information to formulate policies to further promote satisfaction of the customers at different quantiles of satisfaction level. We also compared the prediction accuracies of the regression models at different quantiles. The experiment result showed that, among the seven quantile regression models, the median regression model has the best performance in terms of RMSE, RTIC, and CE performance measures.
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Sánchez, Luis, Víctor Leiva, Helton Saulo, Carolina Marchant, and José M. Sarabia. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications." Mathematics 9, no. 21 (November 1, 2021): 2768. http://dx.doi.org/10.3390/math9212768.

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Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.
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Olsen, Cody S., Amy E. Clark, Andrea M. Thomas, and Lawrence J. Cook. "Comparing Least-squares and Quantile Regression Approaches to Analyzing Median Hospital Charges." Academic Emergency Medicine 19, no. 7 (July 2012): 866–75. http://dx.doi.org/10.1111/j.1553-2712.2012.01388.x.

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Dissertations / Theses on the topic "Median regression, quantile regression"

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RADAELLI, PAOLO. "La Regressione Lineare con i Valori Assoluti." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2004. http://hdl.handle.net/10281/2290.

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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.
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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 erhalten
Generalized 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
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Yu, Keming. "Smooth regression quantile estimation." Thesis, Open University, 1996. http://oro.open.ac.uk/57655/.

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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.
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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.
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Chao, Shih-Kang. "Quantile regression in risk calibration." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17223.

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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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Books on the topic "Median regression, quantile regression"

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Hao, Lingxin, and Daniel Naiman. Quantile Regression. 2455 Teller Road, Thousand Oaks California 91320 United States of America: SAGE Publications, Inc., 2007. http://dx.doi.org/10.4135/9781412985550.

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Davino, Cristina, Marilena Furno, and Domenico Vistocco. Quantile Regression. Oxford: John Wiley & Sons, Ltd, 2014. http://dx.doi.org/10.1002/9781118752685.

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Marilena, Furno, and Vistocco Domenico. Quantile Regression. Chichester, UK: John Wiley & Sons Ltd, 2018. http://dx.doi.org/10.1002/9781118863718.

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Hao, Lingxin. Quantile regression. Thousand Oaks, Calif: Sage Publications, 2007.

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Chernozhukov, Victor. Instrumental variable quantile regression. Cambridge, MA: Massachusetts Institute of Technology, Dept. of Economics, 2006.

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Cleophas, Ton J., and Aeilko H. Zwinderman. Quantile Regression in Clinical Research. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-82840-0.

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McMillen, Daniel P. Quantile Regression for Spatial Data. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31815-3.

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Fitzenberger, Bernd, Roger Koenker, and José A. F. Machado, eds. Economic Applications of Quantile Regression. Heidelberg: Physica-Verlag HD, 2002. http://dx.doi.org/10.1007/978-3-662-11592-3.

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Chernozhukov, Victor. Quantile regression with censoring and endogeneity. Cambridge, MA: National Bureau of Economic Research, 2011.

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Ling, Wodan. Quantile regression for zero-inflated outcomes. [New York, N.Y.?]: [publisher not identified], 2019.

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Book chapters on the topic "Median regression, quantile regression"

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Cleophas, Ton J., and Aeilko H. Zwinderman. "Quantile Regression." In Regression Analysis in Medical Research, 453–67. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61394-5_27.

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Fahrmeir, Ludwig, Thomas Kneib, Stefan Lang, and Brian Marx. "Quantile Regression." In Regression, 597–620. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-34333-9_10.

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Čížek, Pavel. "Quantile Regression." In XploRe® - Application Guide, 19–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57292-0_1.

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Awange, Joseph L., Béla Paláncz, Robert H. Lewis, and Lajos Völgyesi. "Quantile Regression." In Mathematical Geosciences, 359–404. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-67371-4_12.

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Hooten, Mevin B., and Trevor J. Hefley. "Quantile Regression." In Bringing Bayesian Models to Life, 205–20. Boca Raton, FL : CRC Press, Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9780429243653-18.

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Buchinsky, Moshe. "Quantile Regression." In The New Palgrave Dictionary of Economics, 11065–73. London: Palgrave Macmillan UK, 2018. http://dx.doi.org/10.1057/978-1-349-95189-5_2795.

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Buchinsky, Moshe. "Quantile Regression." In The New Palgrave Dictionary of Economics, 1–9. London: Palgrave Macmillan UK, 2008. http://dx.doi.org/10.1057/978-1-349-95121-5_2795-1.

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Buchinksy, Moshe. "Quantile Regression." In Microeconometrics, 202–13. London: Palgrave Macmillan UK, 2010. http://dx.doi.org/10.1057/9780230280816_25.

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Jurečková, Jana. "Regression Quantile and Averaged Regression Quantile Processes." In Analytical Methods in Statistics, 53–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51313-3_3.

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Cleophas, Ton J., and Aeilko H. Zwinderman. "Kernel Regression Versus Quantile Regression." In Quantile Regression in Clinical Research, 241–55. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-82840-0_25.

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Conference papers on the topic "Median regression, quantile regression"

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Formoso, Carolina Rodrigue, Raphael Machado Castilhos, Wyllians Vendramini Borelli, Matheus Zschornack Strelow, and Marcia Fagundes Chaves. "ANTICHOLINERGIC BURDEN IN DEMENTIA." In XIII Meeting of Researchers on Alzheimer's Disease and Related Disorders. Zeppelini Editorial e Comunicação, 2021. http://dx.doi.org/10.5327/1980-5764.rpda031.

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Abstract:
Background: The anticholinergic burden is associated with a greater risk of functional/ cognitive decline and morbidity/mortality. Objectives: Our aim was to quantify the anticholinergic burden in the first visit in our dementia tertiary outpatient clinic. Methods: We performed a retrospective analysis of all first visit medical records of patients referred from primary health care to the outpatient dementia clinic of a tertiary hospital in Porto Alegre with a final diagnosis of dementia or Mild Cognitive Impairment (MCI) between 2014-2019. We evaluated all medications in use and we calculated a final score using Brazilian Anticholinergic Activity Drug (BAAD) score. This scale classified drugs according to its central anticholinergic activity from 1 to 3, with higher values indicating greater activity. The final score is the sum of the score for each drug. We divided the sample in two groups (score=0 and ⩾ 1) and performed a logist regression using age, sex, dementia diagnosis and MMSE as covariates. Results: We identified 199 final diagnoses of dementia (mostly Alzheimer’s Disease (AD) [45.2%]) and 39 of MCI. Most patients with dementia (76.4%) and MCI (74.3%) had at least a BAAD score = 1. Median (IQI) BAAD score was higher in VD, 4 (1.0-6.5). In the regression analysis, BAAD score was associated with MMSE, controlling for covariates. Conclusions: In our sample, the anticholinergic burden was high and correlated with dementia severity.
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Huang, Liqi, Xin Wei, Peikang Zhu, Yun Gao, Mingkai Chen, and Bin Kang. "Federated Quantile Regression over Networks." In 2020 International Wireless Communications and Mobile Computing (IWCMC). IEEE, 2020. http://dx.doi.org/10.1109/iwcmc48107.2020.9148186.

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Kevin Michael Brannan and Donald Paul Butcher. "TMDL Development Using Quantile Regression." In TMDL 2010: Watershed Management to Improve Water Quality Proceedings, 14-17 November 2010 Hyatt Regency Baltimore on the Inner Harbor, Baltimore, Maryland USA. St. Joseph, MI: American Society of Agricultural and Biological Engineers, 2010. http://dx.doi.org/10.13031/2013.35780.

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Bhat, Harish S., Nitesh Kumar, and Garnet J. Vaz. "Towards scalable quantile regression trees." In 2015 IEEE International Conference on Big Data (Big Data). IEEE, 2015. http://dx.doi.org/10.1109/bigdata.2015.7363741.

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Natesan Ramamurthy, Karthikeyan, Kush R. Varshney, and Moninder Singh. "Quantile regression for workforce analytics." In 2013 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2013. http://dx.doi.org/10.1109/globalsip.2013.6737097.

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Fagundes, Roberta A. A., Renata M. C. R. de Souza, and Yanne M. G. Soares. "Quantile regression of interval-valued data." In 2016 23rd International Conference on Pattern Recognition (ICPR). IEEE, 2016. http://dx.doi.org/10.1109/icpr.2016.7900025.

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Ballings, Michel, Dries Benoit, and Dirk Van den Poel. "RFM Variables Revisited Using Quantile Regression." In 2011 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 2011. http://dx.doi.org/10.1109/icdmw.2011.148.

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Dichandra, D., I. Fithriani, and S. Nurrohmah. "Parameter estimation of Bayesian quantile regression." In PROCEEDINGS OF THE 6TH INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES 2020 (ISCPMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0059103.

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Zhou Lihui. "Quantile regression model and application profile." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5622905.

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de Oliveira, Augusto Born, Sebastian Fischmeister, Amer Diwan, Matthias Hauswirth, and Peter F. Sweeney. "Why you should care about quantile regression." In the eighteenth international conference. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2451116.2451140.

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Reports on the topic "Median regression, quantile regression"

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Carlier, Guillaume, Alfred Galichon, and Victor Chernozhukov. Vector quantile regression. Institute for Fiscal Studies, December 2014. http://dx.doi.org/10.1920/wp.cem.2014.4814.

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Lee, Sokbae (Simon), and Le-Yu Chen. Sparse Quantile Regression. The IFS, June 2020. http://dx.doi.org/10.1920/wp.cem.2020.3020.

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Chetverikov, Denis, Yukun Liu, and Aleh Tsyvinski. Weighted-Average Quantile Regression. Cambridge, MA: National Bureau of Economic Research, May 2022. http://dx.doi.org/10.3386/w30014.

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Graham, Bryan, Jinyong Hahn, Alexandre Poirier, and James Powell. Quantile Regression with Panel Data. Cambridge, MA: National Bureau of Economic Research, March 2015. http://dx.doi.org/10.3386/w21034.

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Powell, James L., Alexandre Poirier, Bryan S. Graham, and Jinyong Hahn. Quantile regression with panel data. Institute for Fiscal Studies, March 2015. http://dx.doi.org/10.1920/wp.cem.2015.1215.

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Koenker, Roger. Quantile regression 40 years on. The IFS, August 2017. http://dx.doi.org/10.1920/wp.cem.2017.3617.

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Chernozhukov, Victor, Tetsuya Kaji, and Ivan Fernandez-Val. Extremal quantile regression: an overview. The IFS, December 2017. http://dx.doi.org/10.1920/wp.cem.2017.6517.

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Chernozhukov, Victor, Iván Fernández-Val, and Amanda Kowalski. Quantile Regression with Censoring and Endogeneity. Cambridge, MA: National Bureau of Economic Research, April 2011. http://dx.doi.org/10.3386/w16997.

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Fernandez-Val, Ivan, Victor Chernozhukov, and Amanda Kowalski. Quantile regression with censoring and endogeneity. Institute for Fiscal Studies, May 2011. http://dx.doi.org/10.1920/wp.cem.2011.2011.

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Carlier, Guillaume, Alfred Galichon, and Victor Chernozhukov. Vector quantile regression: an optimal transport approach. Institute for Fiscal Studies, September 2015. http://dx.doi.org/10.1920/wp.cem.2015.5815.

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