MSE-matrix superiority of the mixed over the least squares estimator in the presence of outliers

In his recent paper, Ali (1991) has shown that the mixed regression estimator, when data contain mean-shift or variance inflation outliers, is uniformly superior to the ordinary least squares estimator in terms of scalar-valued mean square error. However, when using the matrix-valued mean square error criterion, this dominance fails to hold in general. The subsequent investigation gives a complete characterization of the situation where the mixed estimator is superior to the LS-estimator when the comparison is made with respect to this stronger MSE-property. Vice versa, the LS-estimator never dominates the mixed estimator relative to this criterion.