Abstract
Empirical Bayes approach to estimation of many parameters is considered. Special features of the techniques discussed are: (i) the handling of unequal sample sizes at various stages of an Empirical Bayes sampling scheme and (ii) a general iterative procedure for estimating the parameters of a parametric prior distribution based on the likelihood approach. Linear empirical Bayes estimation is also considered. Application of the general techniques is demonstrated with special reference to a multinomial data distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aitchison, J. and Shen, S. M. (1980). Logistic-normal distributions: Some properties and uses, Biometrika, 67, 261–272.
Berry, D. A. and Christensen, R. (1979). Empirical Bayes estimation of a bionomial parameter via mixtures of Dirichlet processes, Ann. Statist., 7, 558–568.
DeGroot, M. H. (1970). Optimal Statistical Decisions, McGraw-Hill, New York.
Graybill, F. A. (1969). Introduction to Matrices with Applications in Statistics, Wadsworth, U.S.A.
Griffin, B. S. and Krutchkoff, R. G. (1971). Optimal linear estimators: An empirical Bayes version with application to the binomial distribution, Biometrika, 58, 195–201.
Jackson, D. A., O'Donovan, T. M., Zimmer, W. J. and Deely, J. J. (1970). G 2-minimax estimators in the exponential family, Biometrika, 57, 439–443.
Johns, M. V. (1957). Nonparametric empirical Bayes procedures, Ann. Math. Statist., 28, 649–669.
Leonard, T. (1972). A Bayesian method for histograms, Biometrika, 60, 297–308.
Maritz, J. S. (1970). Empirical Bayes Methods, Methuen, London.
Maritz, J. S. and Lwin, T. (1975). Construction of simple empirical Bayes estimators, J. Roy. Statist. Soc. Ser. B, 37, 421–425.
Martz, H. F. and Lian, M. G. (1974). Empirical Bayes estimation of the binomial parameter, Biometrika, 61, 517–523.
Mosimann, J. (1962). On the compound multinomial distribution, the multivariate β-distribution and correlation among proportions, Biometrika, 49, 65–82.
Robbins, H. (1956). An empirical Bayes approach to statistics, Proc. 3rd Berkeley Symp. Math. Statist. Probability, Vol. I, 157–164, University of California Press, Berkeley, California.
Author information
Authors and Affiliations
About this article
Cite this article
Lwin, T., Maritz, J.S. Empirical Bayes approach to multiparameter estimation: with special reference to multinomial distribution. Ann Inst Stat Math 41, 81–99 (1989). https://doi.org/10.1007/BF00049111
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00049111