Towards a universal self-normalized moderate deviation

被引：15

作者：

Jing, Bing-Yi ^{[1
]}

Shao, Qi-Man ^{[1
,2
]}

Zhou, Wang ^{[3
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Hong Kong, Peoples R China

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[3] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117548, Singapore

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 360卷 / 08期

关键词：

moderate deviation; large deviation; self-normalized sums; the law of the iterated logarithm;

D O I：

10.1090/S0002-9947-08-04402-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is an attempt to establish a universal moderate deviation for self-normalized sums of independent and identically distributed random variables without any moment condition. The exponent term in the moderate deviation is specified when the distribution is in the centered Feller class. An application to the law of the iterated logarithm is given.

引用

页码：4263 / 4285

页数：23

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