Intrinsic losses for empirical Bayes estimation: A note on normal and Poisson cases

Dominique Fourdrinier and Christian P. Robert

Statistics & Probability Letters, 1995, vol. 23, issue 1, 35-44

Abstract: In empirical Bayes analysis, the estimation of the hyperparameter is entirely left to the choice of the experimenter and the corresponding empirical Bayes estimator thus fails to achieve a global coherence. In this paper, we propose a more directed approach based on the use of a formal Bayes hyperprior and of intrinsic losses for the estimation of the hyperparameter. This approach is illustrated in the normal case, where it is shown to lead to an estimator proposed by Alam (1973), and in the Poisson case, when we derive new domination results under the entropy loss.

Keywords: Minimaxity; Entropy; loss; Confluent; hypergeometric; function (search for similar items in EconPapers)
Date: 1995
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