| 非平衡随机效应模型中方差分量的经验Bayes估计 |
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| 引用本文： | 史建红,张常青.非平衡随机效应模型中方差分量的经验Bayes估计[J].数学的实践与认识,2009,39(6). |
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| 作者姓名： | 史建红 张常青 |
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| 作者单位： | 1. 东北财经大学博士后流动站,辽宁,大连,116025;山西师范大学数学与计算机科学学院,山西,临汾,041004
2. 山西师范大学数学与计算机科学学院,山西,临汾,041004 |
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| 基金项目： | 山西省青年科技研究基金，山西师范大学自然科学基金 |
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| 摘 要： | 对非平衡单向分类随机效应模型中方差分量找到了其最小充分统计量,在加权平方损失下导出了其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,并导出了其收敛速度.文末用例子说明了符合定理条件的先验分布是存在的.
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| 关 键 词： | 非平衡单向分类随机效应模型 方差分量 Bayes估计 经验Bayes估计 收敛速度 |
On Empirical Bayes Estimation of Variance Components in Unbalanced Random Effects Models |
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| SHI Jian-hong,ZHANG Chang-qing.On Empirical Bayes Estimation of Variance Components in Unbalanced Random Effects Models[J].Mathematics in Practice and Theory,2009,39(6). |
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| Authors: | SHI Jian-hong ZHANG Chang-qing |
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| Abstract: | Minmal sufficient statistics have been found for unbalanced One-way classification random effect model.under the weighted square loss function,the Bayes estimators of variance components are derived and empirical Bayes estimators are constructed by the kernel estimation method of a multivariate dentity and its mixed partial derivatives.The convergence rates of EB estimators are established under suitable conditions.Finally,an example satisfying the conditions of the main theorem is given. |
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| Keywords: | unbalance One-way classification random effect model variance components Bayes estimators empirical Bayes estimators convergence rates |
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