Abstract
We consider a class of extremal problems for multiple hypothesis testing with set-valued decisions and given total variation distances between hypotheses. The quality of a test is measured by an arbitrary piecewise linear continuous function of the error probabilities. We show that the extremal value of the test quality may be found as a solution of some linear programming problem, so the original infinite-dimensional problem is reduced to a certain finite-dimensional one.
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Savelov, M.P. Extremal problems for hypotheses testing with set-valued decisions. Math. Meth. Stat. 25, 67–77 (2016). https://doi.org/10.3103/S106653071601004X
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DOI: https://doi.org/10.3103/S106653071601004X
Keywords
- multiple hypothesis testing
- non-randomized tests
- total variation distance
- extremal sets of distributions