| 韦来生,王立春.随机效应模型中方差分量渐近最优的经验Bayes估计[J].数学研究及应用,2004,24(4):653~664 |
| 随机效应模型中方差分量渐近最优的经验Bayes估计 |
| Asymptotically Optimal Empirical Bayes Estimation for Variance Components in Random Effects Models |
| 投稿时间：2002-10-14 |
| DOI：10.3770/j.issn:1000-341X.2004.04.010 |
| 中文关键词: 随机效应模型 方差分量 Bayes估计 经验Bayes估计 渐近最优性 |
| 英文关键词:Random effects models variance components Bayes estimators empirical Bayes estimators asymptotic optimality. |
| 基金项目:国家自然科学基金(19971085)和国家教委博士点基金及中科院创新基金资助项目. |
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| 中文摘要: |
| 本文在加权二次损失下导出了双向分类随机效应模型中方差分量的Bayes估计,并利用多元密度函数及其混合偏导数核估计的方法构造了方差分量的经验Bayes(EB)估计.在适当的条件下证明了EB估计的渐近最优性,给出了模型的特例和推广.最后,举出一个满足定理条件的例子. |
| 英文摘要: |
| In this paper, the Bayes estimators of variance components for two-way classification random effects models is derived under weighted quadratic loss function, and the empirical Bayes (EB) estimators are constructed by the kernel estimation of multivariate density and its mixed partial derivatives. The asymptotically optimality of the EB estimators are obtained under some suitable conditions, and the special cases and the generalizations of the model are shown. Finally, an example satisfying the conditions of theorem is given. |
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