I. G. Shevtsova, “Sharpening of the upper-estimate of the absolute constant in the Berry–Esseen inequality”, Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 3,Pages <nobr>622

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Sharpening of the upper-estimate of the absolute constant in the Berry–Esseen inequality

I. G. Shevtsova

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The upper bound of the absolute constant in the classical Berry–Esseen inequality for sums of independent identically distributed random variables with finite third moments is lowered to $C\leqslant 0.7056$.

Keywords: Berry–Esseen inequality, central limit theorem, normal approximation, convergence rate estimate.

Received: 28.06.2006

DOI: 10.4213/tvp46