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Mat. Vopr. Kriptogr., 2018, Volume 9, Issue 3, Pages 45–60 (Mi mvk262)  

New estimates for the variational distance between two distributions of a sample

A. M. Zubkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: For a pair of samples consisting of i.i.d. random variables we obtain new upper and lower bounds for the total variation distance between their distributions. In cases of small distances these estimates are proportional to the total variation distance between distributions of elements of samples and the square root of the sample volume with coefficients depending on the distributions of elements of samples. The results are useful for estimates of the sample volume necessary for testing close hypotheses.

Key words: total variation distance, homogeneous samples, probabilistic inequalities, two-side estimates.

DOI: https://doi.org/10.4213/mvk262

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Document Type: Article
UDC: 519.213.21
Received 11.V.2017

Citation: A. M. Zubkov, “New estimates for the variational distance between two distributions of a sample”, Mat. Vopr. Kriptogr., 9:3 (2018), 45–60

Citation in format AMSBIB
\Bibitem{Zub18}
\by A.~M.~Zubkov
\paper New estimates for the variational distance between two distributions of a sample
\jour Mat. Vopr. Kriptogr.
\yr 2018
\vol 9
\issue 3
\pages 45--60
\mathnet{http://mi.mathnet.ru/mvk262}
\crossref{https://doi.org/10.4213/mvk262}
\elib{http://elibrary.ru/item.asp?id=35601217}


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