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Regular version of the site

Article

A characterization of maximin tests for two composite hypotheses

Mathematical Methods of Statistics. 2015. Vol. 24. No. 2. P. 110-121.

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.