Statistics: Empirical bayes

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Efron and Morris (1973)

Stein's Estimation Rule and Its Competitors--An Empirical Bayes Approach

Bradley Efron; Carl Morris
Journal of the American Statistical Association, Vol. 68, No. 341. (Mar., 1973), pp. 117-130.
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Stein's estimator for k normal means is known to dominate the MLE if k ≥3. In this article we ask if Stein's estimator is any good in its own right. Our answer is yes: the positive part version of Stein's estimator is one member of a class of "good" rules that have Bayesian properties and also dominate the MLE. Other members of this class are also useful in various situations. Our approach is by means of empirical Bayes ideas. In the later sections we discuss rules for more complicated estimation problems, and conclude with results from empirical linear Bayes rules in non-normal cases.