Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis. Issue 2 (March 2015)

• Record Type: Journal Article
• Authors: Elliott, Graham; Müller, Ulrich K.; Watson, Mark W.
• Is Part Of: Econometrica. Volume 83:Issue 2(2015:Mar.)
• Page Start: 771
• Page End: 811
• Publication Date: 2015-03
• Subjects: Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA10535
• Languages: English
• ISSNs: 0012-9682

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>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.</p> </abstract>