A lack-of-fit test for quantile regression process models

Abstract

Quantile regression is a widely used statistical tool for data analysis in practice, but model misspecifications may lead to incorrect inferences. In this paper, a lack-of-fit test for quantile regression processes is proposed for those cases with multivariate covariates, which has not been well studied in the existing literature. An asymptotic result is established, and a numerical study has demonstrated that the proposed method is promising.