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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Testing hypotheses for measures with different masses: Four optimization problems

A. A. Gushchin, S. S. Leshchenko

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Abstract: We consider a problem similar to testing two composite hypotheses, where measures constituting the hypotheses are not

Keywords: Convex duality, testing hypotheses. saddle point.

Bibliography:
and may have different masses. Then it is naturally to consider four different optimization problems. To
characterize optimal solutions we introduce corresponding dual optimization problems. Our main goal is to find sufficient
conditions for the existence of saddle points in each problem.
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