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

<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 seemingly unrelated models (SULREMs) with error terms correlated. Our aim is to find analytical formulas for calculating best unbiased predictors (BLUPs) all unknown parameters two by means solving constrained quadratic matrix optimization problem Löwner sense. We also present variety theoretical statistical properties BLUPs under models.</p>