Shrinkage Positive Rule Estimators for Spherically Symmetrical Distributions

Tn the normal case it is well known that, although the James-Stein rule is minimax, it is not admissible and the associated positive rule is one way to improve on it. We extend this result to the class of the spherically symmetric distributions and to a large class of shrinkage rules. Moreover we propose a family of generalized positive rules. We compare our results to those of Berger and Bock (Statistical Decision Theory and Related Topics, II, Academic Press, New York. 1976). In particular our conditions on the shrinkage estimator are weaker.