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Title: Saddlepoint approximation for student's t-statistic with no moment conditions
Authors: Jing, B.-Y.
Shao, Q.-M. 
Zhou, W. 
Keywords: Absolute error
Asymptotic normality
Edgeworth expansion
Large deviation
Relative error
Saddlepoint approximation
Self-normalized sum
Student's t-statistic
Issue Date: Dec-2004
Citation: Jing, B.-Y., Shao, Q.-M., Zhou, W. (2004-12). Saddlepoint approximation for student's t-statistic with no moment conditions. Annals of Statistics 32 (6) : 2679-2711. ScholarBank@NUS Repository.
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. © Institute of Mathematical Statistics, 2004.
Source Title: Annals of Statistics
ISSN: 00905364
DOI: 10.1214/009053604000000742
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