Shrinkage Estimation

Abstract

Shrinkage estimation developed from the work of Stein for the estimation of the mean of a multivariate normal distribution. The observed vector is, from a decision theory viewpoint, inadmissible. The James–Stein estimator shrinks the observations toward zero. Later work involves estimators shrunk toward the sample mean. Shrinkage estimators are, however, not dominant in problems with a finite sample space, such as the binomial distribution. There are connections with Bayesian and empirical Bayes solutions.