Improving the EBLUPs of balanced mixed-effects models (vol 78, pg 647, 2015)

Lately mixed models are heavily employed in analyses of promotional tactics as well as in clinical research. The Best Linear Unbiased Predictor (BLUP) in mixed models is a function of the variance components, which are typically estimated using conventional MLE based methods. It is well known that such approaches frequently yield estimates of factor variances that are either zero or negative. In such situations, ML and REML either do not provide any EBLUPs, or they all become practically equal, a highly undesirable repercussion. In this article we propose a class of estimators that do not suffer from the negative variance problem, and we do so while improving upon existing estimators. The MSE superiority of the resulting EBLUPs is illustrated by a simulation study. In our derivation, we also introduce a Lemma, which can be considered as the converse of Stein's Lemma.