Choice of hierarchical priors: Admissibility in estimation of normal means

Annals of Statistics

Volumn 24, Issue 3, 1996, Pages 931-951

  Berger, James O ^a   Strawderman, William E ^b  

^a PURDUE UNIVERSITY   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Hyperparameters; Inadmissibility; Mean squared error; Normal hierarchical models; Shrinkage estimation

Indexed keywords

EID: 0030508463     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032526950     Document Type: Article

References (25)

1. ANDREWS, R., BERGER, J. and SMITH, M. (1993). Bayesian estimation of fuel economy potential due to technology improvements. Case Studies in Bayesian Statistics. Lecture Notes in Statist. 83. Springer, New York.
2. ANGERS, J. F. (1987). Development of robust Bayes estimators for a multivariate normal mean. Ph.D. dissertation, Dept. Statistics, Purdue Univ.
3. BARANCHIK, A. (1964). Multiple regression and estimation of the mean of a multivariate normal distribution. Technical Report 51, Dept. Statistics, Stanford Univ.
4. BERGER, J. (1976). Admissible minimax estimation of a multivariate normal mean under arbitrary quadratic loss. Ann. Statist. 4 223-226.
5. BERGER, J. (1980). A robust generalized Bayes estimator and confidence region for a multivariate normal mean. Ann. Statist. 8 716-761.
6. BERGER, J. (1984). The robust Bayesian viewpoint. In Robustness in Bayesian Statistics (J. Kadane, ed.). North-Holland, Amsterdam.
7. BERGER, J. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer, New York.
8. BERGER, J. and BERNARDO, J. (1992a). On the development of the reference prior method. In Bayesian Statistics (J. M. Bernardo, J. O. Berger A. P. Dawid and A. F. M. Smith, eds.) 4 35-60. Oxford Univ. Press.
9. BERGER, J. and BERNARDO, J. (1992b). Reference priors in a variance components problem. Bayesian Analysis in Statistics and Econometrics. Lecture Notes in Statist. 75 177-194.
10. BERGER, J. and DEELY, J. (1988). A Bayesian approach to ranking and selection of related means with alternatives to AOV methodology. J. Amer. Statist. Assoc. 83 364-373.
11. BERGER, J. and ROBERT, C. (1990). Subjective hierarchical Bayes estimation of a multivariate normal mean: on the frequentist interface. Ann. Statist. 18 617-651.
12. BOX, G. E. P. and TIAO, G. C. (1973). Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA.
13. BROWN, L. (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Ann. Math. Statist. 42 855-903.
14. GHOSH, M. (1992). Hierarchical and empirical Bayes multivariate estimation. In Current Issues in Statistical Inference. IMS, Hayward, CA.
15. GOEL, P. K. (1983). Information measures and Bayesian hierarchical models. J. Amer. Statist. Assoc. 78 408-410.
16. GOOD, I. J. (1983). The robustness of a hierarchical model for multinomials and contingency tables. In Scientific Inference, Data Analysis, and Robustness (G. E. P. Box, T. Leonard and C. F. Wu, eds.). Academic Press, New York.
17. HILL, B. (1977). Exact and approximate Bayesian solutions for inference about variance components and multivariate inadmissibility. In New Development in the Application of Bayesian Methods (A. Aykac and C. Brumet, eds.). North-Holland, Amsterdam.
18. JEFFREYS, H. (1961). Theory of Probability. Oxford Univ. Press.
19. KELKER, D. (1970). Distribution theory of spherical distributions and a location-scale parameter. Sankhyā Ser. A 32 419-430.
20. MORRIS, C. (1983). Parametric empirical Bayes inference: theory and applications (with discussion). J. Amer. Statist. Assoc. 78 47-65.
21. STEIN, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. Third Berkeley Symp. Math. Statist. Probab. 1 197-206. Univ. California Press, Berkeley.
22. STRAWDERMAN, W. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Ann. Math. Statist. 42 385-388.
23. STRAWDERMAN, W. (1973). Proper Bayes minimax estimators of the multivariate normal mean for the case of common unknown variances. Ann. Statist. 1 1189-1194.
24. YE, K. (1993). Sensitivity study of the reference priors in a random effect model. Technical report, Dept. Statistics, Virginia Polytechnic Institute and State Univ., Blacksburg.
25. ZHENG, Z. (1982). A class of generalized Bayes minimax estimators. In Statistical Decision Theory and Related Topics (S. S. Gupta and J. Berger, eds.) 3. Academic Press, New York.