ON THE UPPER BOUND FOR THE ABSOLUTE CONSTANT IN THE BERRY-ESSEEN INEQUALITY

被引：39
|
作者：
Korolev, V. Yu. [1 ,2 ]
Shevtsova, I. G. [1 ,2 ]
机构：
[1] Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia
[2] Russian Acad Sci, Inst Informat Problems, Moscow, Russia
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2010年 / 54卷 / 04期
基金：
俄罗斯基础研究基金会;
关键词：
central limit theorem; Berry-Esseen inequality; smoothing inequality; CENTRAL-LIMIT-THEOREM; INDEPENDENT RANDOM-VARIABLES; NORMAL APPROXIMATION; DISTRIBUTIONS; SUMS;
D O I：
10.1137/S0040585X97984449
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
This paper describes the history of the search for unconditional and conditional upper bounds of the absolute constant in the Berry-Esseen inequality for sums of independent identically distributed random variables. Computational procedures are described. New estimates are presented from which it follows that the absolute constant in the classical Berry-Esseen inequality does not exceed 0.5129.
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页码：638 / 658
页数：21
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