Comparison of BLUPs under multiple partitioned linear model and its correctly-reduced models

Abstract

In this study, we investigate the relations between a multiple partitioned linear model and its correctly-reduced models. We consider the comparison problem of covariance matrices of the best linear unbiased predictors (BLUPs) of all unknown vectors including partial parameters under these models by using the block matrix rank and inertia formulas. We derive various inequalities and equalities for covariance matrices of BLUPs under some general assumptions. Also, results for special cases are given.