线性混合效应模型中方差分量的估计

Estimates of Variance Components in Linear Mixed Models with Random Effects

本文首先研究了含三个方差分量的线性混合随机效应模型改进的ANOVA估计,此估计在均方损失下一致优于ANOVA估计,由于这些方差估计取负值的概率大于零,对得到的估计在某非负点采用截尾的方法得到非负估计是一种常用的方法。对文章中提出的估计,研究了此估计在某非负点截尾之后得到的估计在均方损失意义下优于截尾之前的估计的充分条件,同时给出ANOVA估计在截尾之后优于它本身的充分条件,而且将得到的结论推广到更一般的线性混合随机效应模型。

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.