Extension of some important identities in shrinkage-pretest strategies

In this paper, we establish three identities which play a crucial role in deriving the asymptotic distributional risk function and the asymptotic distributional bias of a large class of estimators of a matrix parameter. In particular, we generalize the results in Judge and Bock (The statistical implication of pre-test and Stein-rule estimators in econometrics. North Holland, Amsterdam, <CitationRef CitationID="CR3">1978</CitationRef>). The established results are useful in risk analysis of a class of Stein-rule type matrix estimators. Copyright Springer-Verlag Berlin Heidelberg 2013