Interval estimation for empirical bayes generalizations of Stein's estimator

Carl N. Morris

Expert InsightsPublished 1977

The James-Stein estimator improves the expected mean square error of [k] greater than or equal to three independent sample means for all possible combinations of true means. In spite of this, it is not widely used in practical applications, partly because no confidence intervals accompany it. The author derive interval estimates in this paper based on an uninformative prior distribution and illustrate the use and success of the method in an application. Not only is the estimator about three times as efficient as the sample mean vector in this example, but the intervals provided are 37 percent shorter while containing the true values with greater frequency than nominally claimed. The prior is used in the final section to extend the James-Stein estimator and to provide interval estimates for the case when the unknown parameters are exchangeable but the sample means have unequal variances.

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Morris, Carl N., Interval estimation for empirical bayes generalizations of Stein's estimator. Santa Monica, CA: RAND Corporation, 1977. https://www.rand.org/pubs/papers/P5847.html.
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