Saddlepoint approximations for student's t-statistic without moment conditions

Abstract

Saddlepoint approximations for Student's t-statistics were derived by Daniels and Young (1991) under the indeed stringent exponential moment condition that the underlying density function dies away at least as fast as a normal density in the tails. This is a severe restriction on its applicability. In this thesis, we show that this strong exponential moment restriction can be dispensed off completely, i.e., saddlepoint approximations for the Student's t-statistic remain valid without any moment condition. We also derive saddlepoint approximations for the distribution of Student's t-statistic for lattice random variables without moment conditions. Our results imply that saddlepoint approximations provide very accurate approximations for Student's t-statistic and can be applied much more widely in statistical inference.

The first part of this thesis has been accepted by the Annals of Statistics.

Date of Award	2004
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology