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The James–Stein estimator is a biased estimator of the mean, , of (possibly) correlated Gaussian distributed random variables with unknown means . It arose sequentially in two main published papers.
Empirical Bayes and the James–Stein Estimator. Charles Stein shocked the statistical world in 1955 with his proof that max-imum likelihood estimation methods for Gaussian models, in common use for more than a century, were inadmissible beyond simple one- or two-dimensional situations.
The James-Stein estimator is a significant departure from the “traditional” school of thought which states that the sample mean is the best estimator for the population mean. Stein and James proved that a better estimator than the “perfect” estimator exists, which seems to be somewhat of a paradox.
The best-known example is the James–Stein estimator, which shrinks towards a particular point (such as the origin) by an amount inversely proportional to the distance of from that point. For a sketch of the proof of this result, see Proof of Stein's example.
Nov 19, 2009 · Is there ever a “right” decision? Professor James Stein would argue yes, and in this provocative new book, he shows you how to apply the mathematical principles of Decision Theory to every aspect of your life.
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- James D. Stein
Sep 5, 2013 · We will be using empirical Bayes ideas for estimation, testing, and prediction, beginning here with their path-breaking appearance in the James—Stein formulation. Although the connection was not immediately recognized, Stein's work was half of an energetic post-war empirical Bayes initiative.
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James H. Stein, MD, is the Robert Turell Professor of Cardiovascular Research in the Department of Medicine. He is the director of the UW Health Preventive Cardiology Program and the UW Atherosclerosis Imaging Research Program.
