In this study, we have investigated some comparison problems of the best linear unbiased predictor (BLUP) for a unified form of all unknown parameters in the statistical inference of three competing models according to the mean squared error matrix (MSEM) criteria. Out of the three competing models that we consider: the first model is a linear model with stochastic restriction, the second model is a stochastically restricted linear model with the inclusion of superfluous variables which is obtained from new additions to the first model, and the last model is a stochastically restricted reduced linear model which is a reduced form of the second model. As the comparison operations, we have used the methodology of block matrix inertias and ranks. Furthermore, comparison results for special cases have been demonstrated. We have also illustrated our findings with numerical examples.