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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
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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  • 1. Blyth, C.R. (1986). Approximate binomial confidence limits. J. Amer. Statist. Assoc. 81 843-855; Corridenda (1989), 84, 636. CMP 19:02
  • 2. Daniels, H.E. (1987). Tail probability approximations. Internat. Statist. Rev. 55 37-48. MR 90e:62029
  • 3. Hall, P. (1982). Improving the normal approximation when constructing one-sided confidence intervals for binomial or Poisson parameters. Biometrika 69 647-652. MR 85i:62025
  • 4. Hall, P. (1987). On the bootstrap and continuity correction. J. R. Statist. Soc. B 49 82-89.
  • 5. Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals. Ann. Statist. 16 927-985. MR 89h:62085
  • 6. Lehmann, E.L. (1983). Theory of Point Estimation. Wiley, New York. MR 85a:62001
  • 7. Lehmann, E.L. (1986). Testing Statistical Hypotheses. 2nd. ed., Wiley, New York. MR 87j:62001
  • 8. Loh, W.-Y. (1987). Calibrating confidence coefficients. J. Amer. Statist. Assoc. 82 155-162. MR 88e:62082
  • 9. Loh, W.-Y. (1988). Discussion of ``Theoretical comparison of bootstrap confidence intervals'' by P. Hall. Ann. Statist. 16 972-976.
  • 10. Loh, W.-Y. (1991). Bootstrap calibration for confidence interval construction and selection. Statistica Sinica 1 477-491. CMP 92:02
  • 11. Lugannani, R. and Rice, S. (1980). Saddle point approximation for the distribution of the sum of independent random variables. Adv. Appl. Prob. 12 475-490. MR 81f:60034
  • 12. Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap. Ann. Statist. 9 1187-1195. MR 83c:62047
  • 13. Tingley, M. and Field, C. (1990). Small-sample confidence intervals. J. Amer. Statist. Assoc. 85 427-434. MR 92k:62059
  • 14. Zheng, X. and Loh, W.-Y. (1995). Bootstrapping binomial confidence intervals. J. Statist. Planning and Inference. 43 355-380. MR 96f:62075

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Additional Information

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

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

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