The James-Stein Estimator as an Empirical Bayes Estimator for an Arbitrary Location Family

Abstract

Abstract A well known intuitive justification for the James-Stein estimator of the mean vector of a multivariate normal distribution is that it is an empirical Bayes estimator. The prior distribution is multivariate normal with the mean vector O and covariance matrix equal to σ2 I where σ2 is unknown and is estimated from the data. Here, we derive a version of the James-Stein estimator of the location vector for an essentially arbitrary location family.