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Mathematical Methods of Statistics

, Volume 24, Issue 2, pp 110–121 | Cite as

A characterization of maximin tests for two composite hypotheses

  • A. Gushchin
Article

Abstract

We consider the problem of testing two composite hypotheses in the minimax setting. To find maximin tests, we propose a new dual optimization problem which has a solution under a mild additional assumption. This allows us to characterize maximin tests in considerable generality. We give a simple example where the null hypothesis and the alternative are strictly separated, however, a maximin test is purely randomized.

Keywords

dual problem testing composite hypotheses maximin test 

2000 Mathematics Subject Classification

62F03 62G10 

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Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.International Laboratory of Quantitative FinanceNational Research Univ. Higher School of EconomicsMoscowRussia

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