On second-order optimality of the observed fisher information

Annals of Statistics

Volumn 25, Issue 5, 1997, Pages 2172-2199

  Lindsay, Bruce G ^a   Li, Bing ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b NONE

Author keywords

Ancillarity; Asymptotically linear estimator; Bhattacharyya scores; Bootstrap; Conditional inference; Cumulant; Estimation of loss; Generalized inverse; Jackknife; Observed and expected Fisher information; Sandwich estimators

Indexed keywords

EID: 0031495021     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362393     Document Type: Article

References (40)

1. AMARI, S. (1982). Geometrical theory of asymptotic ancillarity and conditional inference. Biometrika 69 1-17. [Erratum (1983) 70 303.]
2. BARNDOHFF-NIELSEN, O. E. (1980). Conditionality resolutions. Biometrika 67 293-310.
3. BARNDORFF-NIELSEN, O. E. and Cox, D. R. (1994). Inference and Asymptotics. Chapman and Hall, London.
4. BASU, D. (1964). Recovery of ancillary information. Sankhyā Ser. A 20 3-16.
5. BERGER, J. O. (1985a). The frequentist viewpoint and conditioning. In Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer (L. M. LeCam and R. A. Olshen, eds.) 1 15-44. Wadsworth, Monterey, CA.
6. BERGER, J. O. (1985b). In defense of the likelihood principle: axiomatics and coherency. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 33-65. North-Holland, Amsterdam.
7. BHATTACHARYYA, A. (1946). On some analogues to the amount of information and their uses in statistical estimation. Sankhyā 8 1-14.
8. BICKEL, P. J., KLAASSEN, C. A. J., RITOV, Y. and WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press.
9. BROWN, L. D. (1967). The conditional level of Student's t test. Ann. Math. Statist. 38 1068-1071.
10. BROWN, L. D. (1978). A contribution to Kiefer's theory of conditional confidence procedures. Ann. Statist. 6 59-71.
11. BUEHLER, R. J. (1959). Some validity criteria for statistical inference. Ann. Math. Statist. 30 845-863.
12. Cox, D. R. (1958). Some problems connected with statistical inference. Ann. Math. Statist. 29 357-372.
13. EFRON, B. (1975). Defining the curvature of a statistical problem (with application to second order efficiency) (with discussion). Ann. Statist. 3 1189-1242.
14. EFRON, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM, Philadelphia.
15. EFRON, B. and HINKLEY, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information (with discussion). Biometrika 65 457-487.
16. FISHER, R. A. (1974). Statistical Methods and Scientific Inference, 3rd ed. Oliver & Boyd, Edinburgh.
17. GOUTIS, C. and CASELLA, G. (1992). Increasing the confidence in Student's t-interval. Ann. Statist. 20 1501-1513.
18. GOUTIS, C. and CASELLA, G. (1995). Frequentist post-data inference. Internat. Statist. Rev. 63 325-344.
19. HAMPEL, F. R. (1974). The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69 383-393.
20. HJORT, N. L. (1992). On inference in parametric survival data models. Internat. Statist. Rev. 60 355-387.
21. HSIEH, F. and HWANG, J. T. (1993). Admissibility under the frequentist's validity constraint in estimating the loss of the least-squares estimator. J. Multivariate Anal. 44 279-285.
22. HWANG, J. T. and BROWN, L. D. (1991). Estimated confidence under the validity constraint. Ann. Statist. 19 1964-1977.
23. JOHNSTONE, I. (1988). On inadmissibility of some unbiased estimates of loss. In Statistical Decision Theory and Related Topics IV (S. S. Gupta and J. O. Berger, eds.) 1 361-379. Springer, New York.
24. KIEFER, J. (1977). Conditional confidence statements and confidence estimators (with discussion). J. Amer. Statist. Assoc. 72 789-827.
25. KRUSKAL, W. (1975). The geometry of generalized inverses. J. Roy. Statist. Soc. Ser. B 37 272-283.
26. Lu, K. L. and BERGER, J. O. (1989a). Estimation of normal means: frequentist estimation of loss. Ann. Statist. 17 890-906.
27. Lu, K. L. and BERGER, J. O. (1989b). Estimated confidence procedures for multivariate normal means. J. Statist. Plann. Inference 23 1-19.
28. MCCULLAGH, P. (1984). Local sufficiency. Biometrika 71 233-244.
29. MCCULLAGH, P. (1987). Tensor Methods in Statistics. Chapman and Hall, London.
30. PEDERSEN, B. V. (1981). A comparison of the Efron-Hinkley ancillary and the likelihood ratio ancillary in a particular example. Ann. Statist. 9 1328-1333.
31. PIERCE, D. A. (1973). On some difficulties in a frequency theory of inference. Ann. Statist. 1 241-250.
32. REID, N. (1994). A conversation with Sir David Cox. Statist. Sci. 9 439-455.
33. ROBINSON, G. K. (1979a). Conditional properties of statistical procedures. Ann. Statist. 7 742-755.
34. ROBINSON, G. K. (1979b). Conditional properties of statistical procedures for location and scale families. Ann. Statist. 7 756-771.
35. RUKHIN, A. L. (1988a). Estimation loss and admissible loss estimators. In Statistical Decision Theory and Related Topics IV (S. S. Gupta and J. O. Berger, eds.) 1 361-379. Springer, New York.
36. RUKHIN, A. L. (1988b). Loss functions for loss estimation. Ann. Statist. 16 1262-1269.
37. RUKHIN, A. L. (1988c). Estimating the loss of estimators of a binomial parameter. Biometrika 75 153-155.
38. SANDVED, E. (1968). Ancillary statistics and estimation of the loss in estimation problems. Ann. Math. Statist. 39 1755-1758.
39. SKOVGAARD, I. M. (1985). A second-order investigation of asymptotic ancillarity. Ann. Statist. 13, 534-551.
40. SMALL, C. G. and MCLEISH, D. L. (1994). Hilbert Space Methods in Probability and Statistical Inference. Wiley, New York.