A general approach to nonparametric empirical Bayes estimation

Statistics

Volumn 29, Issue 1, 1997, Pages 61-80

  Pensky, Marianna ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Convergence rate; Empirical Bay estimation; Posterior quadratic risk; Reliability characteristics

Indexed keywords

EID: 0039319762     PISSN: 02331888     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331889708802574     Document Type: Article

References (27)

1. Singh, R. S. (1979). Empirical Bayes estimation in Lebesgue-exponential families with rates near the best possible rate. Ann. Statist., 7, 890-902.
2. Fried, J. (1977). Analyses of deoxyribonucleic acid histograms from flow cytofluorometry-estimation of the distribution of cells within s-phase. The Journ. of histochemistry and cytochemistry, 25, 942-951.
3. Bendel, R. B. and Carlin, B. P. (1990). Bayes methods in the ecological fallacy context: estimation of individual correlation from aggregate data. Commun. Statist.-Theory Meth., 19, 2595-2623.
4. Desouza, C. M. (1991). An empirical Bayes formulation of cohort models in cancer epidemiology. Stat. Med., 10, 1241-1256.
5. Mollie, A. and Richardson, S. (1991). Empirical Bayes estimates of cancer mortality rates using spatial models. Stat. Med., 10, 95-112.
6. Lahiri, P. and Park, D. H. (1991). Nonparametric Bayes and empirical Bayes estimators of mean residual life at age t. J. Stat. Plan. Inference, 29, 125-136.
7. Louis, T. A. (1991). Using empirial Bayes methods in biopharmaceutical research. Stat. Med., 10, 811-827.
8. Norberg, R. (1989). Experience rating in group life insurance Scand. Actuarial J., 194-224.
9. Laird, N. (1978). Maximum likelihood estimation of a mixing distribution. JASA 73, 805-811.
10. Zacks, S. (1971). The Theory of Statistical Inference. Wiley. New York.
11. Berger, J. (1988). Statistical Decision Theory and Bayesian Analyses. Springer-Verlag. New York.
12. Robbins, H. (1964). The empirical Bayes approach to statistical decision problems. Ann. Math. Statist., 35, 1-20.
13. Judge, G., Hill, R. S. and Bock, M. E. (1990). An adaptive empirical Bayes estimator of the multivariate normal mean under quadratic loss. J. Econometrics, 44, 189-213.
14. Gao, J. (1990). Empirical Bayes absolute error loss estimation for parameter of uniform distribution families u(θ, cθ). Acta Math. Sinica, 33, 486-496.
15. Tiwari, R. C. and Zalkikar, J. N. (1990). Empirical Bayes estimation of the scale parameter in a Pareto distribution. Comput. Statist. Theory Meth., 19, 2065-2084.
16. Maritz, J. S. and Lwin, T. (1989). Empirical Bayes Methods, Chapman & Hall. London.
17. Walter, G. G. (1981). Orthogonal series estimators of the prior distribution. Sankhya, A43, 228-245.
18. Fan, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problem. Ann. Stat., 19, 1257-1272.
19. Penskaya, M. (1986). Empirical Bayes estimation. Moscow Univ. Math. Bull, 41, 24-28.
20. Robbins, H. (1983). Jerzy Neyman memorial lecture. Some thoughts on empirical Bayes estimation. Ann. Statist, 11, 713-723.
21. Penskaya, M. (1994). On an empirical Bayes estimation of the location parameter. Journ. of Math. Sciences, 72, 2948-2953.
22. Penskaya, M. (1994). On empirical Bayes estimation of the location parameter. Probab. Theory and Its Application, 37, 795-797.
23. Nadaraya, E. A. (1989). Nonparametric estimation of probability densities and regression curves. 20 Kluwer Academic Publishers Group, Dordrecht.
24. Penskaya, M. (1995). On mean square consistent estimation of a ratio. Scandinavian Journ. of Statist, 22 129-137.
25. Antonov, A. V. and Ostreykovskii, V. A. (1993). Estimation of reliability characteristics of elements and systems of the nuclear power equipment by composed methods. Energoatomizdat, Moscow (in Russian).
26. Gradshtein, I. S. and Ryzhik, I. M. (1980). Tables of integrals, series, and products. Academic Press. New York.
27. Erdélyi, A. et al. (1954). Tables of Integral Transforms. Mc Graw-Hill Book Company, New York.