| 平衡线性混合模型方差分量几种估计的优良性 |
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| 引用本文： | 史建红,王松桂.平衡线性混合模型方差分量几种估计的优良性[J].数学年刊A辑(中文版),2005(6). |
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| 作者姓名： | 史建红 王松桂 |
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| 作者单位： | 山西师范大学数学系，北京工业大学应用数理学院 山西 临汾 041004，北京 100022 |
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| 基金项目： | 国家自然科学基金(No．10271010)
北京市自然科学基金(No．1032001)资助的项目 |
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| 摘 要： | 对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方 差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计．同时证明了在此条件下,似然 方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子．
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| 关 键 词： | 平衡线性混合模型 方差分量 最小方差无偏估计 |
OPTIMALITY OF SEVERAL ESTIMATES OF VARIANCE COMPONENTS IN BALANCED LINEAR MIXED MODEL |
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| SHI Jianhong WANG Songgui.OPTIMALITY OF SEVERAL ESTIMATES OF VARIANCE COMPONENTS IN BALANCED LINEAR MIXED MODEL[J].Chinese Annals of Mathematics,2005(6). |
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| Authors: | SHI Jianhong WANG Songgui |
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| Institution: | SHI Jianhong WANG Songgui Department of Mathematics,Shanxi Normal University,Linfen 041004,Shanxi,China. School of Applied Mathematics,Beijing University of Technology,Beijing 100022,China. |
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| Abstract: | For the balanced linear mixed models, a set of easily checking conditions is given for equality of spectral decomposition estimator, minimum norm quadratic unbiased estimator and analysis of variance estimator of variance components. At the same time , it is also shown that the three estimators of variance components are Minimun variance unbiased estimtors and the likelihood equations and restricted likelihood equations have explicit solutions under this conditions. In addition, many linear mixed models which satisfy these condtions are given. |
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| Keywords: | Balanced linear mixed model Variance components Minimun variance unbiased estimtor |
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