Lack-of-fit tests for quantile regression models

• 成果类型: Article
• 署名作者: Dong, Chen; Li, Guodong; Feng, Xingdong
• 署名单位: Shanghai University of Finance & Economics; University of Hong Kong
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12321
• 发表日期: 2019
• 页码: 629-648
• 关键词: Covariance matrices; 2-sample test; inference; dimension; EQUALITY; set

摘要

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.