Minimaxity in estimation of restricted and non-restricted scale parameter matrices

In estimation of the normal covariance matrix, finding a least favorable sequence of prior distributions has been an open question for a long time. This paper addresses the classical problem and accomplishes the specification of such a sequence, which establishes minimaxity of the best equivariant estimator. This result is extended to the estimation of scale parameter matrix in an elliptically contoured distribution model. The methodology based on a least favorable sequence of prior distributions is applied to both restricted and non-restricted cases of parameters, and we give some examples which show minimaxity of the best equivariant estimators under restrictions of scale parameter matrix. Copyright The Institute of Statistical Mathematics, Tokyo 2015