The Berry-Esseen bound for self-normalized sums
type: Item
instance of: scholarly article
title: The Berry-Esseen bound for self-normalized sums
zbMATH Open document ID: 1046.60020
published in: Siberian Advances in Mathematics
publication date: 2004-09-06T00:00:00Z
review text: First, the author estimates a constant in the Berry-Esseen bound for self-normalized sums of independent identically distributed random variables. He obtains different versions of the Berry-Esseen bound, namely, under the assumption of the third or sixth moments and for bounded random variables. His approach to prove the Berry-Esseen bound differs principally from that accepted by V. Bentkus and F. Götze. In the case when sixth moment is finite, the author compares his result with that which can be derived from bounds on the remainder in the two-dimensional central limit theorem.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 2097081
zbMATH Keywords: Student's statistic
zbMATH Keywords: central limit theorem
zbMATH Keywords: standard normal law
zbMATH Keywords: random variable
author: Sergei Nagaev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2097081