A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

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 bec...

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Autores principales:	Luis Sánchez, Víctor Leiva, Helton Saulo, Carolina Marchant, José M. Sarabia
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	likelihood methods local influence diagnostics Monte Carlo simulation R software Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/bbfae4524a2d4e1590a4b7af4c8eb2aa
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spelling	oai:doaj.org-article:bbfae4524a2d4e1590a4b7af4c8eb2aa2021-11-11T18:18:38ZA New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications10.3390/math92127682227-7390https://doaj.org/article/bbfae4524a2d4e1590a4b7af4c8eb2aa2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2768https://doaj.org/toc/2227-7390Standard 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.Luis SánchezVíctor LeivaHelton SauloCarolina MarchantJosé M. SarabiaMDPI AGarticlelikelihood methodslocal influence diagnosticsMonte Carlo simulationR softwareMathematicsQA1-939ENMathematics, Vol 9, Iss 2768, p 2768 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	likelihood methods local influence diagnostics Monte Carlo simulation R software Mathematics QA1-939
spellingShingle	likelihood methods local influence diagnostics Monte Carlo simulation R software Mathematics QA1-939 Luis Sánchez Víctor Leiva Helton Saulo Carolina Marchant José M. Sarabia A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
description	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.
format	article
author	Luis Sánchez Víctor Leiva Helton Saulo Carolina Marchant José M. Sarabia
author_facet	Luis Sánchez Víctor Leiva Helton Saulo Carolina Marchant José M. Sarabia
author_sort	Luis Sánchez
title	A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
title_short	A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
title_full	A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
title_fullStr	A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
title_full_unstemmed	A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications
title_sort	new quantile regression model and its diagnostic analytics for a weibull distributed response with applications
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/bbfae4524a2d4e1590a4b7af4c8eb2aa
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A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

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