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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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2768 |
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| 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 |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:57:08Z |
| format | Article |
| id | doaj.art-bbfae4524a2d4e1590a4b7af4c8eb2aa |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:08Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bbfae4524a2d4e1590a4b7af4c8eb2aa2023-11-22T21:18:34ZengMDPI AGMathematics2227-73902021-11-01921276810.3390/math9212768A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with ApplicationsLuis Sánchez0Víctor Leiva1Helton Saulo2Carolina Marchant3José M. Sarabia4Institute of Statistics, Universidad Austral de Chile, Valdivia 5091000, ChileSchool of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, ChileDepartment of Statistics, Universidade de Brasília, Brasília 70910-900, BrazilFaculty of Basic Sciences, Universidad Católica del Maule, Talca 3480112, ChileDepartment of Quantitative Methods, Universidad CUNEF, 28040 Madrid, SpainStandard 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.https://www.mdpi.com/2227-7390/9/21/2768likelihood methodslocal influence diagnosticsMonte Carlo simulationR software |
| spellingShingle | 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 Mathematics likelihood methods local influence diagnostics Monte Carlo simulation R software |
| title | 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_short | 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 |
| topic | likelihood methods local influence diagnostics Monte Carlo simulation R software |
| url | https://www.mdpi.com/2227-7390/9/21/2768 |
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