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

Authors Zhou, Wang
Issue Date 2004
Summary 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.
Note Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2004
Language English
Format Thesis
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