Sharpening of the upper bound of the absolute constant in the Berry-Esseen inequality

被引：28

作者：

Shevtsova, I. G. ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Lab Math Stat, Dept Computat Math & Cybernet, Moscow 119992, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2007年 / 51卷 / 03期

关键词：

Berry-Esseen inequality; central limit theorem; normal approximation; convergence rate estimate;

D O I：

10.1137/S0040585X97982591

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：

The upper bound of the absolute constant in the classical Berry - Esseen inequality for sums of independent identically distributed random variables with finite third moments is lowered to C (<=) 0.7056.

引用

页码：549 / 553

页数：5

共 16 条

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[2] The accuracy of the Gaussian approximation to the sum of independent variates
Berry, Andrew C.
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[3] Esseen C.G., 1942, ARK MATH ASTR FYS A, V28, P1
[4] Esseen C-G., 1956, SKAND AKTUARIETIDSK, V39, P160, DOI DOI 10.1080/03461238.1956.10414946
[5] Feller W., 1991, An Introduction to Probability Theory and Its Applications, VII
[6] HSU PL, 1944, ANN MATH STAT, V16, P1
[7] Kolmogorov A. N., 1953, VESTNIK MGU, V7, P29
[8] PRAWITZ H, 1975, SCAND ACTUAR J, P145
[9] ROGOZIN BA, 1960, THEOR PROBAB APPL, V5, P114
[10] SHIGANOV IS, 1986, J SOVIET MATH, V35, P109

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