A Further Study of Predictions in Linear Mixed Models

This article is concerned with the prediction problems in linear mixed models (LMM). Both biased predictors and restricted predictors are introduced. It was found that the mean square error matrix (MSEM) of a predictor strongly depends on the MSEM of corresponding estimator of the fixed effects and precise formulas are obtained. As an application, we propose three new predictors to improve the best linear unbiased predictor (BLUP). The performance of the new predictors can be examined easily with the help of vast literature on the linear regression models (LM). We also illustrate our findings with a Monte Carlo simulation and a numerical example.