Saddlepoint approximation for Student's t-statistic with no moment conditions
成果类型：
Article
署名作者：
Jing, BY; Shao, QM; Zhou, W
署名单位：
Hong Kong University of Science & Technology; University of Oregon; National University of Singapore
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053604000000742
发表日期：
2004
页码：
2679-2711
关键词：
摘要：
A saddlepoint approximation of the Student's t-statistic was derived by Daniels and Young [Biometrika 78 (1991) 169-179] under the very stringent exponential moment condition that requires that the underlying density function go down at least as fast as a Normal density in the tails. This is a severe restriction on the approximation's applicability. In this paper we show that this strong exponential moment restriction can be completely dispensed with, that is, saddlepoint approximation of the Student's t-statistic remains valid without any moment condition. This confirms the folklore that the Student's t-statistic is robust against outliers. The saddlepoint approximation not only provides a very accurate approximation for the Student's t-statistic, but it also can be applied much more widely in statistical inference. As a result, saddlepoint approximations should always be used whenever possible. Some numerical work will be given to illustrate these points.