Predictor/estimator computations under a constrained multivariate linear model and some related reduced models

This study deals with basic prediction/estimation issues involving a constrained multivariate linear model (CMLM) and some related reduced models. By reparameterizing these models, the authors create unconstrained multivariate linear models (UMLMs). After that, the authors use some quadratic matrix optimization methods to derive analytical formulas for computing the best linear unbiased predictors/estimators (BLUPs/BLUEs) of all unknown parameter matrices. This provides a broad perspective on BLUPs.