The Stein Phenomenon in Simultaneous Estimation: A Review

Tatsuya Kubokawa
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Tatsuya Kubokawa: Faculty of Economics, University of Tokyo.

No 97-F-14, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: In the simultaneous estimation of a mean of a multivariate normal distribution, Charles Stein discovered the surprising decision-theoretic result that the usual maximum likelihood estimator is inadmissible with respect to quadratic loss in three or more dimensions. Since then, the researches on this Stein phenomenon have received considerable attention. This paper surveys the theoretical study of the Stein phenomenon. The minimaxity of the James-Stein estimator and its improvements are demonstrated instructively, and various extensions and developments in Bayesian frameworks and non-normal distributions are reviewed. The paper shortly refers to the Stein phenomenon in confidence sets and a series of decision-theoretic results in estimation of a covariance matrix.

Pages: 24 pages
Date: 1997-04
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