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

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.The authors gratefully acknowledge the support of Project MTM2016-76969-P (Spanish State Research Agency, AEI) cofunded by the European Regional Development Fund (ERDF). The work of Mercedes Conde-Amboage has been supported by a postdoctoral grant from the Ministry of Culture, Education and University Planning and the Ministry of Economy, Employment and Industry of the Galician Government. Ingrid Van Keilegom gratefully acknowledges support by the European Research Council (2016-2021, Horizon 2020/ERC Grant No. 694409)S