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

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.