| 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.
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