A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

This paper is focused on the goodness-of-fit test of the functional linear composite quantile regression model. A nonparametric test is proposed by using the orthogonality of the residual and its conditional expectation under the null model. The proposed test statistic has an asymptotic standard normal distribution under the null hypothesis, and tends to infinity in probability under the alternative hypothesis, which implies the consistency of the test. Furthermore, it is proved that the test statistic converges to a normal distribution with nonzero mean under a local alternative hypothesis. Extensive simulations are reported, and the results show that the proposed test has proper sizes and is sensitive to the considered model discrepancies. The proposed methods are also applied to two real datasets.