  The main theorem in Judge and Mittelhammer [Judge, G. G., and Mittelhammer,
R. (2004), A Semiparametric Basis for Combining Estimation Problems under
Quadratic Loss; JASA, 99, 466, 479--487] stipulates that, in the context of
nonzero correlation, a sufficient condition for the Stein rule (SR)-type
estimator to dominate the base estimator is that the dimension $k$ should be at
least 5. Thanks to some refined inequalities, this dominance result is proved
in its full generality; for a class of estimators which includes the SR
estimator as a special case. Namely, we prove that, for any member of the
derived class, $k\geqslant 3$ is a sufficient condition regardless of the
correlation factor. We also relax the Gaussian condition of the distribution of
the base estimator, as we consider the family of elliptically contoured
variates. Finally, we waive the condition on the invertibility of the
variance-covariance matrix of the base and the competing estimators. Our
theoretical findings are corroborated by some simulation studies, and the
proposed method is applied to the Cigarette dataset.
