ADAPTIVE TESTING ON A REGRESSION FUNCTION AT A POINT

• 成果类型: Article
• 署名作者: Armstrong, Timothy
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1342
• 发表日期: 2015
• 页码: 2086-2101
• 关键词: asymptotic equivalence; confidence; identification

摘要

We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Holder classes, up to a log log n term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary and the proportion of true null hypotheses in a multiple testing problem.