| 平衡数据结构下ANOVA 估计和SD 估计的比较 |
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| 引用本文： | 吴密霞,孙兵.平衡数据结构下ANOVA 估计和SD 估计的比较[J].中国科学:数学,2013,43(8):751-764. |
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| 作者姓名： | 吴密霞 孙兵 |
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| 作者单位： | 北京工业大学应用数理学院, 北京100124;
北京理工大学数学学院, 北京100081 |
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| 基金项目： | 国家自然科学基金(批准号: 11171011 和11001012);北京市自然科学基金(批准号: 1132007);北京市属高等学校人才强教深化计划“中青年骨干人才培养计划”(批准号: RHR20110820)和北京工业大学校基础研究基金(批准号: X4006013201301)资助项目 |
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| 摘 要： | 在线性混合效应模型下, 方差分析(ANOVA) 估计和谱分解(SD) 估计对构造精确检验和广义P-值枢轴量起着非常重要的作用. 尽管这两估计分别基于不同的方法, 但它们共享许多类似的优点, 如无偏性和有精确的表达式等. 本文借助于已得到的协方差阵的谱分解结果, 揭示了平衡数据一般线性混合效应模型下ANOVA 估计与SD 估计的关系, 并分别针对协方差阵两种结构: 套结构和多项分类随机效应结构, 给出了ANOVA 估计与SD 估计等价的充分必要条件.
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| 关 键 词： | 方差分析(ANOVA) 估计混合效应模型 谱分解(SD)估计 |
Comparison between ANOVA estimator and SD estimator under balanced data |
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| WU MiXia,SUN Bing.Comparison between ANOVA estimator and SD estimator under balanced data[J].Scientia Sinica Mathemation,2013,43(8):751-764. |
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| Authors: | WU MiXia SUN Bing |
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| Abstract: | The analysis of variance (ANOVA) estimator and the spectral decomposition (SD) estimator are very helpful for constructing exact test statistics and generalized P-value pivotal variables under linear mixedeffects models. Though two estimators are constructed with completely different methods, they share many similar advantages, such as unbiased and closed form. In this paper, we make some comparison between ANOVA estimator and SD estimator. Based the spectral decomposition of covariance matrix we have obtained, we discover the relationship between ANOVA estimator and SD estimator, and establish necessary and sufficient conditions for the identity of ANOVA estimator and SD estimator for the models with nest-structure covariance matrix and the models with multi-way crossed classification random effects, respectively. |
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| Keywords: | ANOVA estimator mixed-effects model SD estimator |
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