Saddlepoint approximation for Student’s t-statistic with no moment conditions

Jing, Bing-Yi ; Shao, Qi-Man ; Zhou, Wang

Ann. Statist., Tome 32 (2004) no. 1, p. 2679-2711 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2004-12-14
Classification:  Saddlepoint approximation,  large deviation,  asymptotic normality,  Edgeworth expansion,  self-normalized sum,  Student’s t-statistic,  absolute error,  relative error,  62E20,  60G50