CIRJE-F-52. Kubokawa, Tatsuya and M.S. Srivastava, "Estimating the Covariance Matrix: A New Approach", June 1999.

In this paper, we consider the problem of estimating the covaraince matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available in the sample mean matrix and dominates the James-Stein minimax estimator. Several scale equivariant minimax estimators are also given. This method is then applied to obtain new truncated and improved estimators of the generalized variance; it also provides a new proof to the results of Shorrock and Zidek (1976) and Sinha (1976).