A General Approach to Nonparametric Empirical Bayes Estimation

References

• Singh , R. S. 1979 . Empirical Bayes estimation in Lebesgue-exponential families with rates near the best possible rate . Ann. Statist. , 7 : 890 – 902 .
   Web of Science ®Google Scholar
• 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 .
   PubMed Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Desouza , C. M. 1991 . An empirical Bayes formulation of cohort models in cancer epidemiology . Stat. Med. , 10 : 1241 – 1256 .
   PubMed Web of Science ®Google Scholar
• Mollie , A. and Richardson , S. 1991 . Empirical Bayes estimates of cancer mortality rates using spatial models . Stat. Med. , 10 : 95 – 112 .
   PubMed Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Louis , T. A. 1991 . Using empirial Bayes methods in biopharmaceutical research . Stat. Med. , 10 : 811 – 827 .
   PubMed Web of Science ®Google Scholar
• Norberg , R. 1989 . Experience rating in group life insurance Scand . Actuarial J. , : 194 – 224 .
   Google Scholar
• Laird , N. 1978 . Maximum likelihood estimation of a mixing distribution . JASA , 73 : 805 – 811 .
   Web of Science ®Google Scholar
• Zacks , S. 1971 . The Theory of Statistical Inference , New York : Wiley .
   Google Scholar
• Berger , J. 1988 . Statistical Decision Theory and Bayesian Analyses , New York : Springer-Verlag .
   Google Scholar
• Robbins , H. 1964 . The empirical Bayes approach to statistical decision problems . Ann. Math. Statist. , 35 : 1 – 20 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Gao , J. 1990 . Empirical Bayes absolute error loss estimation for parameter of uniform distribution families u(θ, cθ) . Acta Math. Sinica , 33 : 486 – 496 .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Maritz , J. S. and Lwin , T. 1989 . Empirical Bayes Methods , London : Chapman & Hall .
   Google Scholar
• Walter , G. G. 1981 . Orthogonal series estimators of the prior distribution . Sankhya , A43 : 228 – 245 .
   Google Scholar
• Fan , J. 1991 . On the optimal rates of convergence for nonparametric deconvolution problem . Ann. Stat. , 19 : 1257 – 1272 .
   Web of Science ®Google Scholar
• Penskaya , M. 1986 . Empirical Bayes estimation . Moscow Univ. Math. Bull , 41 : 24 – 28 .
   Google Scholar
• Robbins , H. 1983 . Jerzy Neyman memorial lecture. Some thoughts on empirical Bayes estimation . Ann. Statist , 11 : 713 – 723 .
   Web of Science ®Google Scholar
• Penskaya , M. 1994 . On an empirical Bayes estimation of the location parameter . Journ. of Math. Sciences , 72 : 2948 – 2953 .
   Google Scholar
• Penskaya , M. 1994 . On empirical Bayes estimation of the location parameter . Probab. Theory and Its Application , 37 : 795 – 797 .
   Google Scholar
• Nadaraya , E. A. 1989 . Nonparametric estimation of probability densities and regression curves , Dordrecht : 20 Kluwer Academic Publishers Group .
   Google Scholar
• Penskaya , M. 1995 . On mean square consistent estimation of a ratio . Scandinavian Journ. of Statist , 22 : 129 – 137 .
   Web of Science ®Google Scholar
• Antonov , A. V. and Ostreykovskii , V. A. 1993 . “ Estimation of reliability characteristics of elements and systems of the nuclear power equipment by composed methods ” . In Energoatomizdat Moscow (in Russian)
   Google Scholar
• Gradshtein , I. S. and Ryzhik , I. M. 1980 . Tables of integrals, series, and products , New York : Academic Press .
   Google Scholar
• Erdélyi , A. 1954 . Tables of Integral Transforms , New York : Mc Graw-Hill Book Company .
   Google Scholar