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

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dc.creatorJing, Bing-Yi
dc.creatorShao, Qi-Man
dc.creatorZhou, Wang
dc.date2005-08-30
dc.date.accessioned2026-07-07T08:07:16Z
dc.date.available2026-07-07T08:07:16Z
dc.descriptionA 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0508604
dc.identifierhttp://arxiv.org/abs/math/0508604
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 6, 2679-2711
dc.identifierdoi:10.1214/009053604000000742
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130883
dc.subjectStatistics Theory
dc.subject62E20 (Primary) 60G50. (Secondary)
dc.titleSaddlepoint approximation for Student's t-statistic with no moment conditions
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