Considers the problem of estimating the covariance matrix of a normal distribution. In very large samples the maximum likelihood estimator (MLE) is of course "best" in many respects. In small or moderate samples, however, it is not surprising to find challenges to the MLE's superiority. It is shown that there are admissible estimators which improve upon the MLE, relative to a quadratic loss function, uniformly for all values of the covariance matrix and all sample sizes. 8 pp. Ref.
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