A Cramer type large deviation result for student's t-statistic

被引：70

作者：

Shao, QM ^{[1
]}

机构：

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

来源：

JOURNAL OF THEORETICAL PROBABILITY | 1999年 / 12卷 / 02期

关键词：

t-statistic; asymptotic distribution; self-normalized large deviation;

D O I：

10.1023/A:1021626127372

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：

Let X, X-1, X-2,... be independent and identically distributed random variables with a finite third moment. and let T-n be the Student's t-statistic. This paper shows that lim(n-->infinity) P(T-n > x)/P(t(n) > x) = 1 holds uniformly in 0 less than or equal to x less than or equal to o(n(1/6)), where t(n) has a t-distribution with n - 1 degrees of freedom. An example is also given to show that a finite third moment is necessary for this result.

引用

页码：385 / 398

页数：14

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