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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Better saddlepoint confidence intervals
via bootstrap calibration


Author: Xiaodong Zheng
Journal: Proc. Amer. Math. Soc. 126 (1998), 3669-3679
MSC (1991): Primary 62F25; Secondary 62E20
DOI: https://doi.org/10.1090/S0002-9939-98-04417-7
MathSciNet review: 1452836
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Abstract: Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with $O(n^{-3/2})$ coverage errors, in contrast with $O(n^{-1})$ and $O(n^{-1/2})$ coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.


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Additional Information

Xiaodong Zheng
Affiliation: Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900

DOI: https://doi.org/10.1090/S0002-9939-98-04417-7
Keywords: Bootstrap, hypothesis testing, lattice random variables
Received by editor(s): October 2, 1996
Received by editor(s) in revised form: February 28, 1997
Communicated by: Wei-Yin Loh
Article copyright: © Copyright 1998 American Mathematical Society