Estimates for the accuracy of coupling in the central limit theorem
type: Item
instance of: scholarly article
title: Estimates for the accuracy of coupling in the central limit theorem
zbMATH Open document ID: 0880.60020
DOI: 10.1007/BF02104672
published in: Siberian Mathematical Journal
publication date: 1998-01-06T00:00:00Z
review text: For independent centered random variables \(\xi_1,\ldots,\xi_N\) the author studies the difference \(\Delta={}S/B-Z{}\) where \(S=\sum_{j=1}^N X_j, 0<B^2=\sum_{j=1}^N\text{var} \xi_j<\infty\) and \(Z\) has a standard normal law. More exactly \(S\) and \(Z\) are constructed on some probability space. Under certain conditions the upper bound for \({\mathbf E}\Delta^{\alpha}\exp{(\lambda\Delta/8)}\) is obtained in terms of the modification of Lyapunov's ratio (here \(\alpha\geq 1\) and \(\lambda>0\) is chosen in an appropriate manner). Several estimates for other functions of \(\Delta\) are also established.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 1023933
zbMATH Keywords: rates in the central limit theorem
zbMATH Keywords: modification of the Lyapunov ratio
author: A. I. Sakhanenko
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
cites work: Q4776687
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description: scientific article; zbMATH DE number 1023933