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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 3, Pages 555–564
DOI: https://doi.org/10.4213/tvp95 (Mi tvp95) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

On the accuracy of the normal approximation. II

V. Yu. Korolev, I. G. Shevtsova

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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DOI: https://doi.org/10.4213/tvp95
Abstract: Estimates are presented for the asymptotically exact constants in the estimates of the accuracy of the normal approximation for the distributions of sums of independent identically distributed random variables with finite moments of order $2+\delta$, $0<\delta<1$. Refined practically applicable estimates of the accuracy of the normal approximation are constructed in which the right-hand side is a sum of two summands, the first summand being the Lyapunov fraction with the absolute constant close to the asymptotically exact one, whereas the second summand decreases faster than $n^{-\delta/2}$. Explicit estimates and special “expansions” are given for the second summand.
Keywords: central limit theorem, normal approximation, Berry–Esseen inequality, convergence rate estimate, asymptotically exact constant.
Received: 22.04.2005
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 3, Pages 473–482
DOI: https://doi.org/10.1137/S0040585X97981883
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. II”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 555–564; Theory Probab. Appl., 50:3 (2006), 473–482
Citation in format AMSBIB
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