Saddlepoint approximation for Student's t-statistic with no moment conditions
Abstract
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.
Keywords
Cite
@article{arxiv.math/0508604,
title = {Saddlepoint approximation for Student's t-statistic with no moment conditions},
author = {Bing-Yi Jing and Qi-Man Shao and Wang Zhou},
journal= {arXiv preprint arXiv:math/0508604},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009053604000000742 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)