Simultaneous optimal predictions under two seemingly unrelated linear random-effects models

Abstract

<p style='text-indent:20px;'>This paper considers simultaneous optimal prediction and estimation problems in the context of linear random-effects models. Assume a pair of seemingly unrelated linear random-effects models (SULREMs) with the random-effects and the error terms correlated. Our aim is to find analytical formulas for calculating best linear unbiased predictors (BLUPs) of all unknown parameters in the two models by means of solving a constrained quadratic matrix optimization problem in the Löwner sense. We also present a variety of theoretical and statistical properties of the BLUPs under the two models.</p>