On two-stage shrinkage testtimation

The general procedure of two stage shrinkage testimation formulated in Adlce and Gokhale [Commun. Statist.- Theory Meth. 18, 633-627 (1989)] k further generalized and extended to the multiparameter case. Local optimal-ity result of that paper, in the restricted set up of univariate location families and scalar families, is generalized without any restriction on the parametric family. The local unbiasedness result of that paper is also generalized and in addition local risk- unbiasedness is considered. The optimality and risk-unbiasedness results are proved for the usual matrix loss and their validity for an arbitrary quadratic loss deduced as corollaries.