DIAGNOSTIC TESTS FOR QUANTILE REGRESSION WITH WEIBULL RESPONSE VARIABLES

Abstract

Quantile regression is a valuable tool for modeling the relationship between covariates and the
conditional quantiles of a response variable. However, the validity of quantile regression
inferences relies heavily on the accuracy of the model assumptions. This study focuses on
developing diagnostic tests for quantile regression models with Weibull-distributed response
variables. We propose a series of diagnostic tests based on cumulative residual processes to assess
the adequacy of the quantile regression model. The proposed tests are evaluated through simulation
studies, and their performance is compared to existing methods. The results demonstrate the
importance of checking model assumptions in quantile regression analysis, particularly when
dealing with Weibull response variables. The proposed diagnostic tests are applied to a real dataset
to illustrate their practical utility.
Keywords: Quantile regression, Weibull distribution, diagnostic tests, cumulative residual
processes, model checking.