Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis

2015/01/01 by Graham Elliott, Ulrich K. Müller, Mark W. Watson · 1 voice · 2 citations
Mathematics · Decision Sciences · #Statistical Methods and Inference #Advanced Statistical Process Monitoring #Advanced Statistical Methods and Models

paper · pdf · doi:10.3982/ecta10535

openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

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.

Citations

• THE GENERALIZATION OF ‘STUDENT'S’ PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARLANCES ARE INVOLVED
• Confidence Intervals for Partially Identified Parameters

Cited by

• Short and Simple Confidence Intervals when the Directions of Some Effects are Known
• Semiparametric Testing with Highly Persistent Predictors

Discussions

• The solutions we evaluate are: Nearly-optimal tests (onlinelibrary.wiley.com/doi/abs/10.3...) that target power near β₁₂ = 0 while guarding size. Bias-aware CIs (arxiv.org/abs/2012.14823) or bounds (t [bsky, 0 points, 1 comments]