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A new lack‐of‐fit test for quantile regression with censored data
Author(s) -
CondeAmboage Mercedes,
Van Keilegom Ingrid,
GonzálezManteiga Wenceslao
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12512
Subject(s) - mathematics , quantile regression , test statistic , statistics , quantile , econometrics , test (biology) , statistic , regression analysis , null hypothesis , statistical hypothesis testing , paleontology , biology
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.