Empirical Bayesian estimation of normal variances and covariances

This paper derives and evaluates an algorithm for estimating normal covariances. A particular concern is the performance of the estimator when the dimension of the space exceeds the number of observations. The algorithm is simple, tolerably well founded, and seems to be more accurate for its purpose than the alternatives. Other topics discussed are the joint estimation of variances in one and many dimensions; the loss function appropriate to a variance estimator; and its connection with a certain Bayesian prescription.