"Simultaneous estimation of normal precision matrices"

This paper treats the problem of simultaneously estimating the precision matrices in multivariate normal distributions. A condition for improvement on the unbiased estimators of the precision matrices is derived under a quadratic loss function. The improvement condition is similar to the superharmonic condition established by Stein (1981). The condition allows us not only to provide various alternative estimators such as shrinkage type and enlargement type estimators for the unbiased estimators, but also to present a condition on a prior density under which the resulting generalized Bayes estimators dominate the unbiased estimators. Also, a unified method improving upon both the shrinkage and the enlargement type estimators is discussed.