Statistical Science

The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators

Stephen M. Stigler

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Abstract

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.

Article information

Source
Statist. Sci., Volume 5, Number 1 (1990), 147-155.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177012274

Digital Object Identifier
doi:10.1214/ss/1177012274

Mathematical Reviews number (MathSciNet)
MR1054859

Zentralblatt MATH identifier
0955.62610

JSTOR
links.jstor.org

Keywords
Stein paradox regression James-Stein estimation Poisson distribution admissibility empirical Bayes

Citation

Stigler, Stephen M. The 1988 Neyman Memorial Lecture: A Galtonian Perspective on Shrinkage Estimators. Statist. Sci. 5 (1990), no. 1, 147--155. doi:10.1214/ss/1177012274. https://projecteuclid.org/euclid.ss/1177012274


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