Bounds for probabilities of small relative errors for empirical saddlepoint and bootstrap tail approximations

Annals of Statistics

Volumn 26, Issue 6, 1998, Pages 2369-2394

  Robinson, J ^b   Skovgaard, Ib M ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b NONE

Author keywords

Exponential error rates; Large deviations; Smooth functions of means

Indexed keywords

EID: 0032243133     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1024691475     Document Type: Article

References (19)

1. ALBERS, W., BICKEL, P. J. and VAN ZWET, W. R. (1976). Asymptotic expansions for the power of distribution free tests in the one sample problem. Ann. Statist. 4 108-156.
2. BARNDORFF-NIELSEN, O. (1986). Inference on full or partial parameters based on the standardized signed likelihood ratio. Biometrika 73 307-322.
3. BICKEL, P. J. and VAN ZWET, W. R. (1978). Asymptotic expansions for the power of distribution free tests in the two sample problem. Ann. Statist. 6 937-1004.
4. DANIELS, H. E. and YOUNG, G. A. (1991). Saddlepoint approximation for the studentized mean, with an application to the bootstrap. Biometrika 78 169-179.
5. DAVISON, A. C. and HINKLEY, D. V. (1988). Saddlepoint approximations in resampling methods. Biometrika 75 417-431.
6. DICICCIO, T. J., FIELD, C. A. and FRASER, D. A. S. (1990). Approximations of marginal tail probabilities and inference for scale parameters. Biometrika 77 77-95.
7. DICICCIO, T. J., MARTIN, M. A. and YOUNG, G. A. (1992). Fast and accurate approximate double bootstrap confidence intervals. Biometrika 79 285-295.
8. FEDERER, H. (1969). Geometric Measure Theory. Springer, Berlin.
9. FEUERVERGER, A. (1989). On the empirical saddlepoint approximation. Biometrika 76 457-464.
10. HALL, P. (1990). On the relative performance of the bootstrap and Edgeworth approximations of a distribution function. J. Multivariate Anal. 35 108-129.
11. HALL, P. (1992). The Bootstrap and Edgeworth Expansion. Springer, New York.
12. JENSEN, J. L. (1992). The modified signed log likelihood statistic and saddlepoint approximations. Biometrika 79 693-703.
13. JING, B. Y., FEUERVERGER, A. and ROBINSON, J. (1994). On the bootstrap saddlepoint approximations. Biometrika 81 211-215.
14. JING, B. Y. and ROBINSON, J. (1994). Saddlepoint approximations for marginal and conditional probabilities of transformed variables. Ann. Statist. 22 1115-1132.
15. KOKIC, P. N. (1988). Limit theorems for U-statistics in finite populations. Ph.D. thesis, Univ. Sydney.
16. MCCULLAGH, P. (1987). Tensor methods in statistics. Chapman and Hall, London.
17. PETROV, V. V. (1995). Limit Theorems of Probability Theory. 4 Clarendon Press, Oxford.
18. d. Ann. Probab. 18 727-753.
19. SKOVGAARD, I. M. (1990). Analytic Statistical Models. IMS, Hayward, CA.