An exponential nonuniform Berry-Esseen bound for self-normalized sums

被引:58
作者
Wang, QY [1 ]
Jing, BY
机构
[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia
[2] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China
关键词
Berry-Esseen bound; self-normalized sum; t-statistics; moderate deviation; nonuniform estimate;
D O I
10.1214/aop/1022874829
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
In this paper we shall derive Exponential nonuniform Berry-Esseen bounds in the central limit theorem for self-normalized sums. We show that the size of the error can be reduced considerably by replacing the usual standardization by self-normalization. Tn particular, we establish the exponential bounds for the probability of the self-normalized sums under the condition that the third moment is finite, whereas an exponential moment assumption is required for the standardized sums. Applications to t-statistics and the probabilities of moderate deviations of self-normalized sums are also discussed.
引用
收藏
页码:2068 / 2088
页数:21
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