本文在加权平方损失下导出了单向分类随机效应模型中方差分量 的Bayes估计,利用多元密度及其偏导数的核估计方法构造了方差分量的经验Bayes (EB) 估计,证明了 EB估计的渐近最优性.文末还给出了一个例子说明了符合定理条件的 先验分布是存在的.

In this paper, the Bayes estimators of variance components are derived for one-way classification random effect model under the weighted square loss function, and the empirical Bayes (EB) estimators are constructed by the kernel estimation method of a multivariate density and its mixed partial derivatives. It is shown that the EB estimators are asymptotically optimal. Finally, an example satisfying the conditions of the main theorem is given.