About the Berry-Esseen theorem for weakly dependent sequences
type: Item
instance of: scholarly article
title: About the Berry-Esseen theorem for weakly dependent sequences
zbMATH Open document ID: 0838.60017
DOI: 10.1007/BF01247840
author: Emmanuel Rio
publication date: 1996-05-27T00:00:00Z
review text: We extend the method of Bergström for the rates of convergence in the central limit theorem to weakly dependent sequences. In particular, we prove that, for stationary and uniformly mixing sequences of real-valued and bounded random variables, the rate of convergence in the central limit theorem is of the order of \(n^{- 1/2}\) as soon as the sequence \((\theta_p)_{p > 0}\) of uniform mixing coefficients satisfies \(\sum_{p > 0} p \theta_p < \infty\).
reviewed by: Eduardo García-Río
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 849096
zbMATH Keywords: method of Bergström
zbMATH Keywords: rates of convergence
zbMATH Keywords: central limit theorem
zbMATH Keywords: uniform mixing
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 849096