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

被引：41

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.

引用

页码：638 / 658

页数：21

共 51 条

[1]

BENTKUS V, 1994, J THEORET PROBAB, V7, P211, DOI 10.1007/BF02214268

[2]

BENTKUS V, 1989, LITHUANIAN MATH J, V29, P321

[3]

BENTKUS V, 1991, 91078 U BIEL

[4]

Bergström H, 1949, SKAND AKTUARIETIDSKR, V32, P37