Improved confidence sets for spherically symmetric distributions

The usual confidence set for a multivariate mean vector can be improved upon by recentering the set at a Stein-type estimator: this fact is known to be true under many different distributional assumptions. Thus far, however, the case of unknown variance has not been dealt with analytically. In this paper we prove that recentered set estimators dominate the usual set estimator when sampling is from any of a class of spherically symmetric distributions with unknown variance.