NEARLY OPTIMAL TESTS WHEN A NUISANCE PARAMETER IS PRESENT UNDER THE NULL HYPOTHESIS

• 成果类型: Article
• 署名作者: Elliott, Graham; Mueller, Ulrich K.; Watson, Mark W.
• 署名单位: University of California System; University of California San Diego; Princeton University
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA10535
• 发表日期: 2015
• 页码: 771-811
• 关键词: confidence-intervals; EFFICIENT TESTS; INVARIANT TESTS; inference; regression; models; break; point; size

摘要

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regression coefficient when the sign of a control coefficient is known; small sample inference about the difference in means from two independent Gaussian samples from populations with potentially different variances; inference about the break date in structural break models with moderate break magnitude; predictability tests when the regressor is highly persistent; inference about an interval identified parameter; and inference about a linear regression coefficient when the necessity of a control is in doubt.