Estimates of Variance Components in Linear Mixed Models with Random Effects

In this paper, we propose the improved ANOVA estimates for the linear mixed models with three variance components which are better than ANOVA estimators in the criteria of smaller mean square error (MSE). Based on the fact that the proposed variance estimators are not nonnegative with positive probability, we censor the proposed estimators in some points. Furthermore, we discuss the sufficient conditions to ensure the truncated estimators be nonnegative. The conclusions are extended to more general linear mixed models models with random effects.