Minimax covariance estimation using commutator subgroup of lower triangular matrices

This paper deals with the problem of estimating the normal covariance matrix relative to the Stein loss. The main interest concerns a new class of estimators which are invariant under a commutator subgroup of lower triangular matrices. The minimaxity of a James–Stein type invariant estimator under the subgroup is shown by means of a least favorable sequence of prior distributions. The class yields improved estimators on the James–Stein type invariant and minimax estimator.