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: In the problem of estimating the covariance matrix of a multivariate normal population James and Stein obtained a minimax estimator by considering the best invariant estimator with respect to the triangular group. In this paper its authors propose an orthogonally invariant estimator obtained by averaging the minimax estimator with respect to the invariant measure on the orthogonal group. Explicit forms of the proposed estimator are given for dimensions 2 and 3. Risk is evaluated for various population covariance matrices and it shows a substantial improvement over the minimax estimator for a wide range of population covariance matrices.

An orthogonally invariant minimax estimator of the covariance matrix of a multivariate normal population