A Berry-Esseen bound for student's statistic in the non-iid case

被引：36

作者：

Bentkus, V ^{[1
]}

Bloznelis, M ^{[1
]}

Gotze, F ^{[1
]}

机构：

[1] VILNIUS STATE UNIV, DEPT MATH, LT-2006 VILNIUS, LITHUANIA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 1996年 / 9卷 / 03期

关键词：

Student's statistic; Berry-Esseen bound; non-identically distributed random variables; convergence rate; Central Limit Theorem; self-normalized sums;

D O I：

10.1007/BF02214086

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：

We establish a Berry-Esseen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esseen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.

引用

页码：765 / 796

页数：32

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