When you're estimating something about some object that's a member of a larger group of similar objects (say, the batting average of a baseball player, who belongs to a baseball team), how should you estimate it: use measurements of the individual, or get some extra information from the group? The James-Stein estimator tells you how to combine individual and group information make predictions that, taken over the whole group, are more accurate than if you treated each individual, well, individually.
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