SHRINKAGE POSITIVE RULE ESTIMATORS FOR SPHERICALLY SYMMETRICAL DISTRIBUTIONS

Tn the normal case it is well known that, although the James-Stein rul e 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 s pherically symmetric distributions and to a large class of shrinkage r ules. Moreover we propose a family of generalized positive rules. We c ompare our results to those of Berger and Bock (Statistical Decision T heory and Related Topics, II, Academic Press, New York. 1976). In part icular our conditions on the shrinkage estimator are weaker. (C) 1995 Academic Press. Inc.