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.