Geodesic
Two-sided estimates for the sum of probabilities of errors in the multiple hypotheses testing problem with finite number of hypotheses about a nonhomogeneous sample
Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 405-416 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: multiple hypothesis testing, probability inequality, two-sided estimate.
Mots-clés : total variation distance 
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M. P. Savelov. Two-sided estimates for the sum of probabilities of errors in the multiple hypotheses testing problem with finite number of hypotheses about a nonhomogeneous sample. Teoriâ veroâtnostej i ee primeneniâ, Tome 69 (2024) no. 2, pp. 405-416. http://geodesic.mathdoc.fr/item/TVP_2024_69_2_a11/

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