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.

Stein's Paradox

Linear Digressions