Academic literature on the topic 'M-quantile'

Health-related quality of life assessment is important in the clinical evaluation of patients with metastatic disease that may offer useful information in understanding the clinical effectiveness of a treatment. To assess if a set of explicative variables impacts on the health-related quality of life, regression models are routinely adopted. However, the interest of researchers may be focussed on modelling other parts (e.g. quantiles) of this conditional distribution. In this paper, we present an approach based on quantile and M-quantile regression to achieve this goal. We applied the methodologies to a prospective, randomized, multi-centre clinical trial. In order to take into account the hierarchical nature of the data we extended the M-quantile regression model to a three-level random effects specification and estimated it by maximum likelihood.

We derive the semiparametric efficiency bound in dynamic models of conditional quantiles under a sole strong mixing assumption. We also provide an expression of Stein’s (1956) least favorable parametric submodel. Our approach is as follows: First, we construct a fully parametric submodel of the semiparametric model defined by the conditional quantile restriction that contains the data generating process. We then compare the asymptotic covariance matrix of the MLE obtained in this submodel with those of the M-estimators for the conditional quantile parameter that are consistent and asymptotically normal. Finally, we show that the minimum asymptotic covariance matrix of this class of M-estimators equals the asymptotic covariance matrix of the parametric submodel MLE. Thus, (i) this parametric submodel is a least favorable one, and (ii) the expression of the semiparametric efficiency bound for the conditional quantile parameter follows.

The purpose of this work is twofold: on the one hand, recent methodologies will be used to estimate technical efficiency and its determinants factors in Spain's retail sector. In particular, the order-m approach, which is based on the concept of expected minimum input function and quantile regression, for the analysis of the factors determinants of efficiency is used. On the other hand, the results obtained applying the methods mentioned in the Spanish retail sector can contribute to opening up a new field of analysis since the results may be compared by means of the methodologies proposed as well as those which already exist in the literature. The paper used data envelopment analysis stochastic (order-m) to measure efficiency and quantile regression analysis for the second stage in Spanish retail. For the second stage of analysis relative of the factors determinants of efficiency, we use quantile regression. We take account of heterogeneity between the different characteristics of firms, using quantile regression techniques. We find that firm size, age and market concentration are positively related to the efficiency along the quantiles considered in the analysis. The relationship between intensity of capital and better trained employees in the efficiency shows a curvilinear behavior. Also, there are significant differences by region to which the firm belongs. The main contribution of this paper is to provide an efficiency analysis for Spanish retail sector using a non parametric approach with a robust estimator and quantile regression analysis for second stage. This methodology allows for a more careful analysis of what happens at firm level.

Metode Small Area Estimations (SAE) digunakan sebagai pendekatan yang reliabel dalam mengatasi kendala ketidakcukupan sampel pada survei sampel. BPS memproduksi statistik area kecil menggunakan metode SAE popular seperti Empirical Best Linear Unbiased Prediction dalam model Fay-Herriot (EBLUP-FH). Metode EBLUP-FH sebagai pendekatan parametrik memerlukan asumsi normalitas dan terbebas dari outliers pada kedua komponen random effect-nya. Namun, hal tersebut sulit dipenuhi karena seringkali data di lapangan berperilaku ekstrim. Metode SAE M-quantile Chambers-Dunstan (CD) merelaksasi asumsi parametrik dan robust dalam inferensi terhadap outliers. Penelitian ini mengkaji metode M-quantile CD dalam meningkatkan robustness pendugaan area kecil melalui penerapannya pada data riil untuk estimasi rata-rata pengeluaran rumah tangga per kapita tingkat kecamatan di DI Yogyakarta tahun 2018. Penelitian ini menggunakan data Susenas 2018 dan Podes 2018. Hasil implementasi pada data riil menunjukkan model M-quantile CD berhasil memperbaiki presisi EBLUP-FH. Dengan mengimplementasikan M-quantile CD diharapkan estimasi data berperilaku ekstrim lebih akurat untuk pengambilan kebijakan di daerah.

This paper examines the impact of chief executive officer (CEO) and deal characteristics on mergers and acquisitions (M&A) duration in Malaysia. Univariate analysis and quantile regression (QR) are performed on 556 completed M&As transactions undertaken by Malaysian public firms from 2001 to 2019. In line with the upper echelons theory, which states that organizational outcomes can be predicted by looking at the characteristics of top-level executives, the findings from QR show that CEO characteristics significantly affect acquisition duration. This effect is conditional on the duration quantiles for CEO tenure and CEO duality but non-conditional for foreign CEO. Specifically, the findings reveal that the degree of influence by CEO characteristics gets stronger when the transactions are longer and complicated. CEO tenure can decrease M&A duration when a transaction falls in longer duration quantile. M&A transactions tend to take a longer duration when there is CEO duality. Foreign CEOs show more ability to execute transactions in a short duration compared to local CEOs. Deal characteristics such as deal size, merger transaction, hiring a financial advisor and conducting multiple acquisitions are main factors that prolong duration. The findings of this study may benefit policymakers, managers, and investors who involve directly and indirectly in an M&A process.

Abstract Questo lavoro di tesi ha come finalità lo sviluppo e l’implementazione di un modello semiparametrico M-quantile ad effetti random che sia in grado di cogliere l’eventuale presenza di un trend spaziale nei dati ambientali. Il modello proposto è una estensione del modello M-quantile ad effetti casuali di base in cui è stata inclusa una componente spaziale. La componente spaziale è modellata combinando insieme un’intercetta random (Chambers e Tzavidis, 2006) che coglie l’effetto del gruppo e un termine semiparametrico per catturare la regolarità residua nello spazio (Pratesi et al. 2009). Quest’ultima componente è trattata mediante una spline bivariata delle coordinate geografiche dei siti di campionamento. Come proposto da Rupert et al. (2003), i coefficienti dei nodi della spline bivariata sono trattati come effetti random. L’approccio di massima verosimiglianza robusta (Richardson and Welsh, 1995) e uno metodo sequenziale a due stadi è stato adottato per ottenere la stima dei parametri del modello (Tzavidis et al., 2015). Tre studi di simulazione basati sul modello sono stati condotti per verificare la prestazioni di stima e predittive ma anche per confrontare il modello proposto con il modello non-parametrico M-Quantile P-spline. Infine, il modello è stato apllicato a dati di concentrazione di Radon indoor della regione Lombardia.
In this work a M-quantile regression approach (Breckling and Chambers, 1988) is proposed to evaluate their impact at different level of the response variable. In particular, we extend the basic M-quantile model to include a spatial component in addition to other covariates. The spatial component is modelled by combining a random intercept (Chambers and Tzavidis, 2006) to catch the lithology effect on IRC and a semiparametric term, which is expected to grasp residual regularities across space (Pratesi et al. 2009). The flexible component is modeled via a thin-plate bivariate spline of the geographical coordinates (longitude and latitude) of the sampling sites. Akin to Ruppert et al. (2003), we propose to treat the coefficients of the knots of the bivariate spline as a further random component in order to obtain smoother results. A robust maximum likelihood approach (Richardson and Welsh, 1995) has been adopted to estimate the model using the two-stage algorithm proposed by Tzavidis et al. (2015). Three model-based simulations were carried out to confirm estimation and predictives performance and to compare the semiparametric M-Quantile random effect with alternative approach at the problem. The model is applied to a sample of IRC measures collected in two successive radon campaigns in Lombardy.

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.

L'objet de cette thèse est d'établir des résultats asymptotiques pour l'estimateur du quantile conditionnel par la méthode des polynômes locaux ainsi qu'à la généralisation de ces résultats pour les M-estimateurs. Nous étudions ces estimateurs et plus particulièrement leur représentation de Bahadur et leur biais. Nous donnons en outre un résultat sur les intervalles de confiance uniformes construits à partir de cette représentation pour le quantile conditionnel et ses dérivées.

Dans cette de thèse, nous nous intéressons à la modélisation non paramétrique de données extrêmes spatiales. Nos résultats sont basés sur un cadre principal de la théorie des valeurs extrêmes, permettant ainsi d’englober les lois de type Pareto. Ce cadre permet aujourd’hui d’étendre l’étude des événements extrêmes au cas spatial à condition que les propriétés asymptotiques des estimateurs étudiés vérifient les conditions classiques de la Théorie des Valeurs Extrêmes (TVE) en plus des conditions locales sur la structure des données proprement dites. Dans la littérature, il existe un vaste panorama de modèles d’estimation d’événements extrêmes adaptés aux structures des données pour lesquelles on s’intéresse. Néanmoins, dans le cas de données extrêmes spatiales, hormis les modèles max stables,il n’en existe que peu ou presque pas de modèles qui s’intéressent à l’estimation fonctionnelle de l’indice de queue ou de quantiles extrêmes. Par conséquent, nous étendons les travaux existants sur l’estimation de l’indice de queue et des quantiles dans le cadre de données indépendantes ou temporellement dépendantes. La spécificité des méthodes étudiées réside sur le fait que les résultats asymptotiques des estimateurs prennent en compte la structure de dépendance spatiale des données considérées, ce qui est loin d’être trivial. Cette thèse s’inscrit donc dans le contexte de la statistique spatiale des valeurs extrêmes. Elle y apporte trois contributions principales. • Dans la première contribution de cette thèse permettant d’appréhender l’étude de variables réelles spatiales au cadre des valeurs extrêmes, nous proposons une estimation de l’indice de queue d’une distribution à queue lourde. Notre approche repose sur l’estimateur de Hill (1975). Les propriétés asymptotiques de l’estimateur introduit sont établies lorsque le processus spatial est adéquatement approximé par un processus M−dépendant, linéaire causal ou lorsqu'il satisfait une condition de mélange fort (a-mélange). • Dans la pratique, il est souvent utile de lier la variable d’intérêt Y avec une co-variable X. Dans cette situation, l’indice de queue dépend de la valeur observée x de la co-variable X et sera appelé indice de queue conditionnelle. Dans la plupart des applications, l’indice de queue des valeurs extrêmes n’est pas l’intérêt principal et est utilisé pour estimer par exemple des quantiles extrêmes. La contribution de ce chapitre consiste à adapter l’estimateur de l’indice de queue introduit dans la première partie au cadre conditionnel et d’utiliser ce dernier afin de proposer un estimateur des quantiles conditionnels extrêmes. Nous examinons les modèles dits "à plan fixe" ou "fixed design" qui correspondent à la situation où la variable explicative est déterministe et nous utlisons l’approche de la fenêtre mobile ou "window moving approach" pour capter la co-variable. Nous étudions le comportement asymptotique des estimateurs proposés et donnons des résultats numériques basés sur des données simulées avec le logiciel "R". • Dans la troisième partie de cette thèse, nous étendons les travaux de la deuxième partie au cadre des modèles dits "à plan aléatoire" ou "random design" pour lesquels les données sont des observations spatiales d’un couple (Y,X) de variables aléatoires réelles. Pour ce dernier modèle, nous proposons un estimateur de l’indice de queue lourde en utilisant la méthode des noyaux pour capter la co-variable. Nous utilisons un estimateur de l’indice de queue conditionnelle appartenant à la famille de l’estimateur introduit par Goegebeur et al. (2014b)
In this thesis, we investigate nonparametric modeling of spatial extremes. Our resultsare based on the main result of the theory of extreme values, thereby encompass Paretolaws. This framework allows today to extend the study of extreme events in the spatialcase provided if the asymptotic properties of the proposed estimators satisfy the standardconditions of the Extreme Value Theory (EVT) in addition to the local conditions on thedata structure themselves. In the literature, there exists a vast panorama of extreme events models, which are adapted to the structures of the data of interest. However, in the case ofextreme spatial data, except max-stables models, little or almost no models are interestedin non-parametric estimation of the tail index and/or extreme quantiles. Therefore, weextend existing works on estimating the tail index and quantile under independent ortime-dependent data. The specificity of the methods studied resides in the fact that theasymptotic results of the proposed estimators take into account the spatial dependence structure of the relevant data, which is far from trivial. This thesis is then written in thecontext of spatial statistics of extremes. She makes three main contributions.• In the first contribution of this thesis, we propose a new approach of the estimatorof the tail index of a heavy-tailed distribution within the framework of spatial data. This approach relies on the estimator of Hill (1975). The asymptotic properties of the estimator introduced are established when the spatial process is adequately approximated by aspatial M−dependent process, spatial linear causal process or when the process satisfies a strong mixing condition.• In practice, it is often useful to link the variable of interest Y with covariate X. Inthis situation, the tail index depends on the observed value x of the covariate X and theunknown fonction (.) will be called conditional tail index. In most applications, the tailindexof an extreme value is not the main attraction, but it is used to estimate for instance extreme quantiles. The contribution of this chapter is to adapt the estimator of the tail index introduced in the first part in the conditional framework and use it to propose an estimator of conditional extreme quantiles. We examine the models called "fixed design"which corresponds to the situation where the explanatory variable is deterministic. To tackle the covariate, since it is deterministic, we use the window moving approach. Westudy the asymptotic behavior of the estimators proposed and some numerical resultsusing simulated data with the software "R".• In the third part of this thesis, we extend the work of the second part of the framemodels called "random design" for which the data are spatial observations of a pair (Y,X) of real random variables . In this last model, we propose an estimator of heavy tail-indexusing the kernel method to tackle the covariate. We use an estimator of the conditional tail index belonging to the family of the estimators introduced by Goegebeur et al. (2014b)

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.

The goal of this thesis is to bridge the gap between univariate and multivariate quantiles by extending the study of univariate quantile regression and its generalizations to multivariate responses. The statistical analysis focuses on a multivariate framework where we consider vector-valued quantile functions associated with multivariate distributions, providing inferential procedures and establishing the asymptotic properties of the proposed estimators. We illustrate their applicability in a wide variety of scientific settings, including time series, longitudinal and clustered data. The dissertation is divided into four chapters, each of them focusing on various aspects of multivariate analysis and different data types and structures. The methodologies we propose are supported by theoretical results and illustrated using simulation studies and real-world data.

Strong hurricanes, such as Camille in 1969, Andrew in 1992, and Katrina in 2005, cause catastrophic damage. It is important to have an estimate of when the next big one will occur. You also want to know what influences the strongest hurricanes and whether they are getting stronger as the earth warms. This chapter shows you how to model hurricane intensity. The data are basinwide lifetime highest intensities for individual tropical cyclones over the North Atlantic and county-level hurricane wind intervals. We begin by considering trends using the method of quantile regression and then examine extreme-value models for estimating return periods. We also look at modeling cyclone winds when the values are given by category, and use Miami-Dade County as an example. Here you consider cyclones above tropical storm intensity (≥ 17 m s−1) during the period 1967–2010, inclusive. The period is long enough to see changes but not too long that it includes intensity estimates before satellite observations. We use “intensity” and “strength” synonymously to mean the fastest wind inside the cyclone. Consider the set of events defined by the location and wind speed at which a tropical cyclone first reaches its lifetime maximum intensity (see Chapter 5). The data are in the file LMI.txt. Import and list the values in 10 columns of the first 6 rows of the data frame by typing . . . > LMI.df = read.table("LMI.txt", header=TRUE) > round(head(LMI.df)[c(1, 5:9, 12, 16)], 1). . . The data set is described in Chapter 6. Here your interest is the smoothed intensity estimate at the time of lifetime maximum (WmaxS). First, convert the wind speeds from the operational units of knots to the SI units of meter per second. . . . > LMI.df$WmaxS = LMI.df$WmaxS * .5144 . . . Next, determine the quartiles (0.25 and 0.75 quantiles) of the wind speed distribution. The quartiles divide the cumulative distribution function (CDF) into three equal-sized subsets. . . . > quantile(LMI.df$WmaxS, c(.25, .75)) 25% 75% 25.5 46.0 . . . You find that 25 percent of the cyclones have a lifetime maximum wind speed less than 26 m s−1 and 75 percent have a maximum wind speed less than 46ms−1, so that 50 percent of all cyclones have a maximum wind speed between 26 and 46 m s−1 (interquartile range–IQR).

At-site flood frequency analysis (FFA) of extreme hydrological events under Bayesian paradigm has been carried out and compared with frequentist paradigm of maximum likelihood estimation (MLE). The main objective of this chapter is to identify the best approach between Bayesian and frequentist one for at-site FFA. As a case study, the data of only two stations were used, Kotri and Rasul, and Bayesian and MLE approaches were implemented. Most commonly used tests were applied for checking initial assumptions. Goodness of fit (GOF) tests were used to identify the best model, which indicated that the generalized extreme value (GEV) distribution appeared to be best fitted for both stations. Under Bayesian paradigm, quantile estimates are constructed using Markov Chain Monte Carlo (MCMC) simulation method for their respective returned periods and non-exceedance probabilities. For MCMC simulations, as compared to other sampler, the M-H sampling technique was used to generate a large number of parameters. The analysis indicated that the standard errors of the parameters' estimates and ultimately the quantiles' estimates using Bayesian methods remained less as compared to maximum likelihood estimation (MLE), which shows the superiority of Bayesian methods over conventional ones in this study. Further, the safety amendments under two techniques were also calculated, which also show the robustness of Bayesian method over MLE. The outcomes of these analyses can be used in the selection of better design criteria for water resources management, particularly in flood mitigation.

Regional frequency analysis (RFA) based on L-moments is applied to the HIPOCAS hindcast data using daily maximum significant wave heights offshore Portugal to identify the homogeneous regions and to suggest the appropriate regional frequency distribution and extreme quantiles. Several statistics are computed at the various grid points in the area of study to classify the wave conditions of the regions. The daily maximum significant wave heights of the rough winter month January are used for this case study. The results of the study have shown that there are 3 homogeneous regions in the offshore region under investigation (35°–45°N, −9.5°–−11°W) comprising from 15 equally spaced grid points referring to an area of 0.25°×0.25°. It is interesting to observe that the algorithm is able to identify neighboring grid points as members of different regions. The maximum discrepancy between the at-sites’ extreme quantiles and their respective regional quantiles is 0.82 m for a return period of 100 years.