Nearly optimal tests when a nuisance parameter is present under the null hypothesis

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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.

Original languageEnglish (US)
Pages (from-to)771-811
Number of pages41
JournalEconometrica
Volume83
Issue number2
DOIs
StatePublished - Mar 1 2015

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Keywords

  • Least favorable distribution
  • composite hypothesis
  • maximin tests

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