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|Title: ||Saddlepoint approximations for student's t-statistic without moment conditions|
|Authors: ||Zhou, Wang|
|Issue Date: ||2004 |
|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.|
|Description: ||Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2004|
vii, 82 leaves : ill. ; 30 cm
HKUST Call Number: Thesis MATH 2004 Zhou
|Appears in Collections:||MATH Doctoral Theses|
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