Comparison of predictors under constrained general linear model and its future observations

Abstract

. This study deals with some basic inference problems about future observations in a general linear model (GLM) with linear parameter constraints, known as a constrained general linear model (CGLM). Combining the CGLM and its future observations, the author turns the model into a reparameterized form. Using some quadratic matrix optimization methods, the author derives analytical formulas for calculating the best linear unbiased predictors (BLUPs) of all unknown parameter matrices under a CGLM and its future observations. In particular, the author next gives a comprehensive search on the comparison of dispersion matrices of BLUPs of unknown vectors by establishing various equalities and inequalities for dispersion matrices of BLUPs under the model by using elementary block matrix operations and some formulas of rank and inertia of block matrices.