Two-sided Estimates for the Sum of Probabilities of Errors in the Multiple Hypothesis Testing Problem with Finite Number of Hypotheses on a Nonhomogeneous Sample
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Abstract
Theory of Probability &Its Applications, Volume 69, Issue 2, Page 322-330, August 2024. We obtain two-sided estimates for the weighted sum of probabilities of errors in the multiple hypothesis testing problem with finite number of hypotheses on a nonhomogeneous sample of size $n$. The obtained upper and lower estimates are shown to converge to zero exponentially fast with increasing $n$ in a wide class of cases. The results obtained can be used for deriving two-sided estimates for the size of a sample required for multiple hypothesis testing.
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Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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