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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 2, Pages 440–445 (Mi tvp2312)

Short Communications

On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$

V. V. Senatov

Moscow

Abstract: We obtain an estimate of the order $O(n^{-1/2)}$ for the rate of convergence with respect to the balls in the central limit theorem in $R^k$. The main part of the estimate does not depend on the dimensional parameter $k$. This estimate accounts the closeness of the distributions of summands to the normal distribution.

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English version:
Theory of Probability and its Applications, 1984, 2:2, 463–467

Bibliographic databases:

Citation: V. V. Senatov, “On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$”, Teor. Veroyatnost. i Primenen., 28:2 (1983), 440–445; Theory Probab. Appl., 2:2 (1984), 463–467

Citation in format AMSBIB
\Bibitem{Sen83} \by V.~V.~Senatov \paper On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in $R^k$ \jour Teor. Veroyatnost. i Primenen. \yr 1983 \vol 28 \issue 2 \pages 440--445 \mathnet{http://mi.mathnet.ru/tvp2312} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=700227} \zmath{https://zbmath.org/?q=an:0569.60022} \transl \jour Theory Probab. Appl. \yr 1984 \vol 2 \issue 2 \pages 463--467 \crossref{https://doi.org/10.1137/1128042}