COE-F-126 (March 2006)
Kubokawa, Tatsuya,
"Characterization of Priors in the Stein Problem"
Abstract
The so-called Stein problem is addressed in the estimation of a mean vector of a multivariate normal distribution
with a known covariance matrix. For general prior distributions with sphericity, the paper derives conditions on
priors under which the resulting generalized Bayes estimators are minimax. It is also shown that the conditions can
be expressed based on the inverse Laplace transform of the general prior. The relationsip between Stein's super-
harmonic condition and the general conditions is discussed. Finally, a characterization of the priors for the
admissibility is given, and admissible and minimax estimators are developed.