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Biometrika 1966 53(3-4):417-429; doi:10.1093/biomet/53.3-4.417
© 1966 by Biometrika Trust
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Smooth empirical Bayes estimation for one-parameter discrete distributions

J. S. MARITZ

Department of Statistics, University of Melbourne Victoria, Australia

A study is made of the simple empirical Bayes estimators proposed by Robbins (1956). These estimators are compared with ‘best’ conventional estimators in terms of their expected squared error ‘loss’. The object of the study is to determine the amount of prior data which would be needed for the empirical Bayes estimator to be preferred to the conventional estimator. It is concluded that the required number of previous observations is likely to be too large for the simple empirical Bayes estimators to be useful in practice. Smooth empirical Bayes estimators are proposed, which make more effective use of prior results. A method of smoothing is developed which is besed on estimating a step function approximation to the prior distribution of the parameter. Some examples are studied in detail, and the results indicate that these smooth empirical Bayes estimators are potentially useful in practice.


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[Abstract]


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