"Minimaxity in Estimation of Restricted and Non-restricted Scale Parameter Matrices"

In estimation of the normal covariance matrix, nding a least favorable sequence of prior distributions has been an open question for a long time. In this paper, we address the classical problem and succeed in construction of such a sequence, which establishes minimaxity of the best equivariant estimator. We also derive unied conditions for a sequence of prior distributions to be least favorable in the general estimation problem with an invariance structure. These unied conditions are applied to both restricted and non-restricted cases of parameters, and we give a couple of examples which show minimaxity of the best equivariant estimators under restrictions of the covariance matrix.