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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Bibliographic Details
Published in:Mathematics (Basel) 2021-11, Vol.9 (21), p.2768
Main Authors: Sánchez, Luis, Leiva, Víctor, Saulo, Helton, Marchant, Carolina, Sarabia, José M.
Format: Article
Language:English
Subjects:
Asymmetry
Asymptotic methods
Asymptotic properties
Datasets
Generalized linear models
Impact analysis
likelihood methods
local influence diagnostics
Maximum likelihood estimators
Maximum likelihood method
Monte Carlo simulation
Parameter estimation
Perturbation
Quantiles
R software
Regression models
Skewed distributions
Statistical analysis
Weibull distribution
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9212768