On the maximum likelihood estimation of a covariance matrix (Q722606)

Stein phenomena (or Stein paradox) is as followed: ``there is a better estimator than the sample mean vector in the case of the multinormal mean vector under a quadratic loss function, and there is a better estimator than the sample covariance matrix in the case of multinormal covariance matrix under the Stein loss function.'' In this paper the set of the diagonal matrices is taken rather than the set of triangular matrices, and it was adopted to the Stein's approach. Iwasawa decomposition is used to enhance Stein's phenomenon under the Stein loss function and MLE based on the Iwasawa decomposition is led to minimaxity.