Uniform approximation of bayes solutions and posteriors: Frequentistly valid bayes inference

Statistics and Risk Modeling

Volumn 15, Issue 1, 1997, Pages 51-74

[No Author Info available]

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041805910     PISSN: 21931402     EISSN: 21967040     Source Type: Journal    
DOI: 10.1524/strm.1997.15.1.51     Document Type: Article

References (33)

1. Berger, J. (1980),“A robust generalized Bayes estimator and confidence region for a multivariate normal mean,” Ann. Statist., 8, pp. 716-761.
2. Berger, J. (1985),“Statistical Decision Theory and Bayesian Analysis,” 2nd ed., New York: Springer,.
3. Berger, J. and Robert, C. (1990),“Subjective hierarchical Bayes estimation of a multivariate normal mean: on the frequentist interface,” Ann. Statist., 18, pp. 617-651.
4. Bickel, P.J. and Yahav, J.A. (1969),“Some contributions to the asymptotic theory of Bayes solutions,” Z. Wahrsch. verω. Geb., 11, pp. 257-276.
5. Brown, L.D. (1966),“On the admissibility of invariant estimators of one or more location parameters,” Ann. Math. Statist., 37, pp. 1087-1136.
6. Brown, L.D. (1971),“Admissible estimators, recurrent diffusions, and insoluble boundary value problems,” Ann. Math. Statist., 42, pp. 855-904.
7. Brown, L.D. and Hwang, J.T. (1982),“A unified admissibility proof,” in Statistical Decision Theory and Related Topics III,S.S. Gupta and J. Berger (eds.), New York: Academic Press.
8. Casella, G. and Berger, R.L. (1987),“Reconciling Bayesian and frequentist evidence in the one-sided testing problem,” J. Amer. Statist. Assoc., 82, pp. 106-111.
9. DasGupta, A. and Rubin, H. (1986),“Bayesian estimation subjeect to minimaxity of the mean of a multivvariate normal distribution in the case of a common unknown variance: a case for Bayesian robustness,” Statistical Decision Theory and Related Topics, S.S. Gupta and J. Berger (eds.), Vol.2, pp. 325-346, New York: Springer Verlag
10. DasGupta, A. and Studden, W.J. (1989),“Frequentist behavior of robust Bayes estimates of normal means,” Statist, and Decisions, 7, pp. 333-361.
11. Dugundji, J. (1975), Topology, London: Prentice Hall.
12. Efron, B. and Morris, C. (1971),“Limiting the risk of Bayes and empirical Bayes estimators—Part I: The Bayes case,” J. Amer. Statist. Assoc., 87, pp. 130-139.
13. Ghosh, M. (1992),“Hierarchical and Empirical Bayes multivariate estimation,” in IMS Lecture Notes, M. Ghosh and P.K. Pathak (eds.) pp. 151-177.
14. Ghosh, J.K., Mukerjee, R. (1991),“Characterization of priors under which Bayesian and frequentist Bartlett corrections are equivalent in the multiparameter case,” J. Multivariate Anal., 38 no. 2, pp. 385-393.
15. Ghosh, J.K., Sinha, B.K., and Joshi, S.N. (1982),“Expansions for posterior probability and integrated Bayes risk,” Statistical Decision Theory and Related Topics III,S.S. Gupta and J. Berger (eds.), New York: Academic Press.
16. Hartigan, J. A. (1966)“Note on the confidence prior of Welch and Peers,” J. Roy. Statist. Soc. Ser. B, 28, pp. 55-56.
17. Ibragimov, I.A. and Khas'minsky, R.Z. (1972),“Asymptotic behavior of statistical estimators. II. Limit theorems for the a posteriori density and Bayes estimators,” Theory of Prob. and Its Appl, 18, pp. 76-91.
18. Ibragimov, I.A. and Khas'minsky, R.Z. (1981), Statistical Estimation: Asymptotic Theory, New York: Springer.
19. Johnson, R.A. (1967),“An asymptotic expansion for posterior distributions Arm. Math. Statist., 38, pp. 1899-1906.
20. Kadane, J.B. and Chuang, D.T. (1978),“Stable Decision problems,” Ann. Statist., 6, pp. 1095-1110.
21. Lehmann, E.L. (1983), Theory of Point Estimation, New York: Wiley.
22. Lehmann, E.L. (1986), Testing Statistical Hypotheses, New York: Wiley.
23. Meeden, G. and Isaacson, D. (1977),“Approximate behavior of the posterior distribution for a large observation,” Ann. Statist., 5, pp. 899-905.
24. Rubin, D.B. (1984),“Bayesianly justifiable and relevant frequency calculations for applied statistician.” Ann. Statist., 12, pp. 1151-1172.
25. Stein, C. (1985),“On the coverage probability of confidence sets based on a prior distribution,” Sequential Meth. Statist., 16, pp. 485-514Banach Center Publications.
26. Strawderman, W.E. (1971),“Proper Bayes minimax estimators of the multivariate normal mean Ann. Math. Statist., 42, pp. 385-388.
27. Strawderman, W.E. and Cohen, A. (1971),“Admissibility of estimators of the mean vector of a multivariate normal distribution with quadratic loss Ann. Math. Statist., 42, pp. 270-296.
28. Umbach, D. (1978),“On the approximate behavior of the posterior distribution for an extreme multivariate observation,” J. Mult. Anal., 8, pp. 518-531.
29. Walker, A.M. (1969),“On the asymptotic behavior of posterior distributions,” J. Roy. Statist. Soc. Ser. B, 31, pp. 80-88.
30. Welch, B. L. and Peers, H. W. (1963)“On formulae for confidence points based on integrals of weighted likelihoods,” J. Roy. Statist. Soc. Ser. B, 25, pp. 318-329.
31. Woodroofe, M. (1976),“Frequentist properties of Bayesian sequential tests Biometrika, 63, pp. 101-110.
32. Woodroofe, M. (1989),“Very weak expansions for sequentially designed experiments: linear models,” Ann. Statist., 17, pp. 1087-1102.
33. Zidek, J.V. (1970),“Sufficient conditions for the admissibility under squared-error loss of formal Bayes estimators,” Ann. Math. Statist., 41, pp. 446-456.