The 𝑟-𝑑 class predictions in linear mixed models

In this paper, we propose the r-d class predictors which are general predictors of the best linear unbiased predictor (BLUP), the principal components regression (PCR) and the Liu predictors in the linear mixed models. Superiorities of the linear combination of the new predictors to each of these predictors are done in the sense of the mean square error matrix criterion. Finally, numerical examples and a simulation study are done to illustrate the findings.