Testing monotonicity of regression

• 成果类型: Article
• 署名作者: Ghosal, S; Sen, A; van der Vaart, W
• 署名单位: Vrije Universiteit Amsterdam; University of Hyderabad
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1054-1082
• 关键词: u-processes; density; CONVERGENCE; statistics; limit; sums

摘要

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.