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Bayesian Robustness and the Stein Effect

1982; Volume: 77; Issue: 378 Linguagem: Inglês

10.1080/01621459.1982.10477818

1537-274X

James O. Berger,

Statistical Methods and Bayesian Inference

Abstract In simultaneous estimation of normal means, it is shown that through use of the Stein effect surprisingly large gains of a Bayesian nature can be achieved, at little or no cost, if the prior information is misspecified. This provides a justification, in terms of robustness with respect to mis-specification of the prior, for employing the Stein effect, even when combining a priori independent problems (i.e., problems in which no empirical Bayes effects are obtainable). To study this issue, a class of minimax estimators that closely mimic the conjugate prior Bayes estimators is introduced.