Improved minimax predictive densities under Kullback-Leibler loss

Annals of Statistics

Volumn 34, Issue 1, 2006, Pages 78-91

  George, Edward I ^a   Liang, Feng ^b   Xu, Xinyi ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b DUKE UNIVERSITY   (United States)

^c OHIO STATE UNIVERSITY   (United States)

Author keywords

Bayes rules; Heat equation; Inadmissibility; Multiple shrinkage; Multivariate normal; Prior distributions; Shrinkage estimation; Superharmonic marginals; Superharmonic priors; Unbiased estimate of risk

Indexed keywords

EID: 33744815939     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000155     Document Type: Article

References (24)

1. AITCHISON, J. (1975). Goodness of prediction fit. Biometrika 62 547-554. MR0391353
2. ASLAN, M. (2002). Asymptotically minimax Bayes predictive densities. Ph.D. dissertation, Dept. Statistics, Yale Univ.
3. BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed. Springer, New York. MR0804611
4. BROWN, L. D. (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problems. Ann. Math. Statist. 42 855-903. MR0286209
5. BROWN, L. D., DASGUPTA, A., HAFF, L. R. and STRAWDERMAN, W. E. (2006). The heat equation and Stern's identity: Connections, applications. J. Statist. Plann. Inference 136 2254-2278.
6. FOURDRINIER, D., STRAWDERMAN, W. E. and WELLS, M. T. (1998). On the construction of Bayes minimax estimators. Ann. Statist. 26 660-671. MR1626063
7. GEORGE, E. I. (1986). Minimax multiple shrinkage estimation. Ann. Statist. 14 188-205. MR0829562
8. GEORGE, E. I. (1986). Combining minimax shrinkage estimators. J. Amer. Statist. Assoc. 81 437-445. MR0845881
9. GEORGE, E. I. (1986). A formal Bayes multiple shrinkage estimator. Camm. Statist. A-Theory Methods 15 2099-2114. MR0851859
10. HARRIS, I. R. (1989). Predictive fit for natural exponential families. Biometrika 76 675-684. MR1041412
11. HARTIGAN, J. A. (1998). The maximum likelihood prior. Ann. Statist. 26 2083-2103. MR 1700222
12. KOMAKI, F. (1996). On asymptotic properties of predictive distributions. Biometrika 83 299-313. MR 1439785
13. KOMAKI, F. (2001). A shrinkage predictive distribution for multivariate normal observables. Biometrika 88 859-864. MR 1859415
14. KOMAKI, F. (2004). Simultaneous prediction of independent Poisson observables. Ann. Statist. 321744-1769. MR2089141
15. LEHMANN, E. L. and CASELLA, G. (1998). Theory of Point Estimation, 2nd ed. Springer, New York. MR 1639875
16. LIANG, F. (2002). Exact minimax procedures for predictive density estimation and data compression. Ph.D. dissertation, Dept. Statistics, Yale Univ.
17. LIANG, F. and BARRON, A. (2004). Exact minimax strategies for predictive density estimation, data compression and model selection. IEEE Trans. Inform. Theory 50 2708-2726. MR2096988
18. MURRAY, G. D. (1977). A note on the estimation of probability density functions. Biometrika 64150-152. MR0448690
19. No, V. M. (1980). On the estimation of parametric density functions. Biometrika 67 505-506. MR0581751
20. STEELE, J. M. (2001). Stochastic Calculus and Financial Applications. Springer, New York. MR1783083
21. STEIN, C. (1974). Estimation of the mean of a multivariate normal distribution. InProc. Prague Symposium on Asymptotic Statistics (J. Hájek, ed.) 2 345-381. Univ. Karlova, Prague. MR0381062
22. STEIN, C. (1981). Estimation of the mean of a multivariate normal distribution. Ann. Statist. 9 1135-1151. MR0630098
23. STRAWDERMAN, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Ann. Math. Statist. 42 385-388. MR0397939
24. SWEETING, T. J., DATTA, G. S. and GHOSH, M. (2006). Nonsubjective priors via predictive relative entropy regret. Ann. Statist. 34 441-468.