A lack-of-fit test for quantile regression

• 成果类型: Article
• 署名作者: He, XM; Zhu, LX
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Hong Kong; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214503000000963
• 发表日期: 2003
• 页码: 1013-1022
• 关键词: model checks; Nonparametric Regression; linear-regression; median regression; hypothesis; Cusum

摘要

We propose an omnibus lack-of-fit test for linear or nonlinear quantile regression based on a cusum process of the gradient vector. The test does not involve nonparametric smoothing but is consistent for all nonparametric alternatives without any moment conditions on the regression error. In addition, the test is suitable for detecting the local alternatives of any order arbitrarily close to n(-1/2) from the null hypothesis. The limiting distribution of the proposed test statistic is non-Gaussian but can be characterized by a Gaussian process. We propose a simple sequential resampling scheme to carry out the test whose nominal levels are well approximated in our empirical study for small and modest sample sizes.