Lack‐of‐fit tests for quantile regression models. (29th April 2019)

• Record Type: Journal Article
• Authors: Dong, Chen; Li, Guodong; Feng, Xingdong
• Is Part Of: Journal of the Royal Statistical Society. Volume 81:Number 3(2019)
• Page Start: 629
• Page End: 648
• Publication Date: 2019-04-29
• Subjects: High dimensional data -- Hypothesis test -- Lack of fit -- Quantile regression -- Two‐sample test; Statistics -- Periodicals; Great Britain -- Statistics -- Periodicals; 519.2
• DOI: 10.1111/rssb.12321
• Languages: English
• ISSNs: 1369-7412

Abstract

Summary: The paper novelly transforms lack‐of‐fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two‐sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test can maintain the power when the number of covariates exceeds the sample size. The null distribution of the high dimensional test has an explicit form, and the p ‐values or critical values can then be calculated directly. The finite sample performance of the tests proposed is examined by simulation studies, and their usefulness is further illustrated by two real examples.