| Saddlepoint approximations for student's t-statistic without moment conditions (2004) | |||||||||||
Abstract | |||||||||||
| Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2004. vii, 82 leaves : ill. ; 30 cm. HKUST Call Number: Thesis MATH 2004 Zhou. 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. | |||||||||||
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