A characterization of maximin tests for two composite hypotheses
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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.
Keywordsdual problem testing composite hypotheses maximin test
2000 Mathematics Subject Classification62F03 62G10
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