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Point Optimal Testing: A Survey of the Post 1987 Literature

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  • Maxwell L. King
  • Sivagowry Sriananthakumar

Abstract

In the absence of uniformly most powerful (UMP) tests or uniformly most powerful invariant (UMPI) TESTS, King (1987c) suggested the use of Point Optimal (PO) tests, which are most powerful at a chosen point under the alternative hypothesis. This paper surveys the literature and major developments on point optimal testing since 1987 and suggests some areas for future research. Topics include tests for which all nuisance parameters have been eliminated and dealing with nuisance parameters via (i) a weighted average of p values, (ii) approximate point optimal tests, (iii) plugging in estimated parameter values, (iv) using asymptotics and (v) integration. Progress on using point-optimal testing principles for two-sided testing and multi-dimensional alternatives is also reviewed. The paper concludes with thoughts on how best to deal with nuisance parameters under both the null and alternative hypotheses, as well as the development of a new class of point optimal test for multi-dimensional testing.

Suggested Citation

  • Maxwell L. King & Sivagowry Sriananthakumar, 2015. "Point Optimal Testing: A Survey of the Post 1987 Literature," Monash Econometrics and Business Statistics Working Papers 5/15, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2015-5
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp05-15.pdf
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    Keywords

    Local to unity asymptotics; Neyman-Pearson lemma; nuisance parameters; power envelope; unit root testing.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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