Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models

This paper considers comparison problems of predictor and estimator in the context of seemingly unrelated regression models (SURMs). SURMs are a class of multiple regression equations with correlated errors among the equations from linear regression models. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) and the ordinary least squares predictors (OLSPs) of unknown vectors under SURMs by using various rank and inertia formulas of block matrices. The results for comparisons of the best linear unbiased estimators (BLUEs) and the ordinary least squares estimators (OLSEs) in the models are also considered.