V. V. Senatov, “On the estimate of the rate of convergence with respect to the system of balls in the central limit theorem in <nobr>$R^k$</nobr>”, Teor. Veroyatnost. i Primenen., 1983, Volume 28, Issue 2,Pages <nobr>440

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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.

Received: 17.12.1982