Abstract
The technical validity of the saddlepoint technique for approximating the resampling distribution of the sample mean of i.i.d. and non-i.i.d. random variables is examined. The relative errors are shown to occur at the same rate as in parametric analysis. Disereteness in resampling problems is accounted for. The uniformity of the errors is also explored.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barndorff-Nielsen, O. and Cox, D. R. (1979). Edgeworth and saddlepoint approximations with statistical applications (with discussion), J. Roy. Statist. Soc. Ser. B, 41, 279–312.
Daniels, H. E. (1954). Saddlepoint approximations in statistics, Ann. Math. Statist., 25, 631–650.
Daniels, H. E. (1983). Saddlepoint approximations for estimating equations, Biometrika, 70, 89–96.
Daniels, H. E. (1987). Tail probability approximations, Internat. Statist. Rev., 55, 37–48.
Davison, A. C. and Hinkley, D. V. (1988). Saddlepoint approximations in resampling methods, Biometrika, 75, 417–431.
Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans, CBMS-NSF Monograph 38, SIAM, Philadelphia.
Hall, P. (1988). Theoretical comparison of bootstrap confidence intervals (with discussion), Ann. Statist., 16, 927–953.
Jeffreys, H. and Jeffreys, B. S. (1962). Methods of Mathematical Physics, 3rd ed., Cambridge Univ. Press, London-New York.
Jensen, J. L. (1988). Uniform saddlepoint approximations, Adv. in Appl. Probab., 20, 622–634.
Lugannani, R. and Rice, S. O. (1980). Saddlepoint approximations for the distribution of the sum of independent random variables, Adv. in Appl. Probab., 12, 475–490.
Miller, R. G.Jr. (1986). Beyond ANOVA, Basics of Applied Statistics, Wiley, New York.
Petrov, V. V. (1975). Sums of Independent Random Variables, (translated by A. A. Brown), Springer, New York.
Reid, N. (1988). Saddlepoint methods and statistical inference (with discussion), Statist. Sci., 3, 213–238.
Robinson, J. (1982). Saddlepoint approximations for permutation tests and confidence intervals, J. Roy. Statist. Soc. Ser. B, 44, 91–101.
Singh, K. (1981). On the asymptotic accuracy of Efron's bootstrap, Ann. Statist., 9, 1187–1195.
Wang, S. (1988). Saddlepoint approximations in statistics, including resampling, Ph.D. dissertation, The University of Texas at Austin.
Author information
Authors and Affiliations
Additional information
This work was completed while the author was at the University of Texas at Austin.
About this article
Cite this article
Wang, S. Saddlepoint approximations in resampling analysis. Ann Inst Stat Math 42, 115–131 (1990). https://doi.org/10.1007/BF00050783
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00050783