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The main theorem in Judge and Mittelhammer [Judge, G. G., and Mittelhammer,R. (2004), A Semiparametric Basis for Combining Estimation Problems underQuadratic Loss; JASA, 99, 466, 479--487] stipulates that, in the context ofnonzero correlation, a sufficient condition for the Stein rule (SR)-typeestimator to dominate the base estimator is that the dimension $k$ should be atleast 5. Thanks to some refined inequalities, this dominance result is provedin its full generality; for a class of estimators which includes the SRestimator as a special case. Namely, we prove that, for any member of thederived class, $k\geqslant 3$ is a sufficient condition regardless of thecorrelation factor. We also relax the Gaussian condition of the distribution ofthe base estimator, as we consider the family of elliptically contouredvariates. Finally, we waive the condition on the invertibility of thevariance-covariance matrix of the base and the competing estimators. Ourtheoretical findings are corroborated by some simulation studies, and theproposed method is applied to the Cigarette dataset.

On Combining Estimation Problems Under Quadratic Loss: A Generalization