A new lack‐of‐fit test for quantile regression with censored data

Abstract

A new lack-of-fit test for quantile regression models will be presented for the case where the response variable is right-censored. The test is based on the cumulative sum of residuals, and it extends the ideas of He and Zhu (2003) to censored quantile regression. It will be shown that the empirical process associated with the test statistic converges to a Gaussian process under the null hypothesis and is consistent. To approximate the critical values of the test, a bootstrap mechanism will be used.A simulation study will be carried out to study the performance of the new test in comparison with other tests available in the literature. Finally, a real data application will be presented to show the good properties of the new lack-of-fit test in practice. K E Y W O R D Sbootstrap calibration, censored data, lack-of-fit tests, quantile regression INTRODUCTIONAlthough mean regression is still a traditional benchmark in regression studies, the quantile approach is receiving increasing attention, because it allows a more complete description of the conditional distribution of the response given the covariate, and it is more robust to deviations from error normality. That is, while classical regression gives only information on the conditional

Finite sample and asymptotic distributions of a statistic for sufficient follow‐up in cure models

“…For an alternative nonparametric fitting, see López‐Cheda, Amalia & de Ullibarri (2021). See Conde‐Amboage, Van Keilegom & González‐Manteiga (2021) and their references for goodness‐of‐fit tests for parametric models with censored data. Knowledge of the (estimated) exact distribution allows for simulation of percentiles or moments, via MCMC, for example.…”

Confidence Band Estimation for Survival Random Forests

“…Hall and Wellner (1980) applies the weak convergence of the Kaplan-Meier survival estimator to a Gaussian process with a specific covariance functional to form simultaneous confidence bands. Many other papers also use Gaussian processes as asymptotic convergence of survival functions and obtain confidence bands (Bose and Sen, 2002;Zhu et al, 2002;Conde-Amboage et al, 2021). However, the calculations of these confidence bands are not straightforward, particularly in Koul and Ling (2006).…”