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February, 1990 The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators
Stephen M. Stigler
Statist. Sci. 5(1): 147-155 (February, 1990). DOI: 10.1214/ss/1177012274


More than 30 years ago, Charles Stein discovered that in three or more dimensions, the ordinary estimator of the vector of means of a multivariate normal distribution is inadmissible. This article examines Stein's paradox from the perspective of an earlier century and shows that from that point of view the phenomenon is transparent. Furthermore, this earlier perspective leads to a relatively simple rigorous proof of Stein's result, and the perspective can be extended to cover other situations, such as the simultaneous estimation of several Poisson means. The relationship of this perspective to other earlier work, including the empirical Bayes approach, is also discussed.


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Stephen M. Stigler. "The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators." Statist. Sci. 5 (1) 147 - 155, February, 1990.


Published: February, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62610
MathSciNet: MR1054859
Digital Object Identifier: 10.1214/ss/1177012274

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1990
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