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1、多元重复测量模型和估计的比较【摘要】：对试验单元重复测量得到的数据称为重复测量数据。重复测量数据分析在卫生和生命科学、流行病学、生物医学研究等许多领域有着广泛的应用。本论文致力于研究多变量重复测量模型及估计的比较问题。论文的内容分为三个部分。第一部分：考虑完全数据的多变量重复测量方差分析模型(MRMANOV A)。完全数据的 MRM 设计是指对每个试验个体在每一时间点都进行测量。MRM 是 RM 的推广，它允许每次测量得到的观察值是一个向量。响应变量在 p 种情形下进行测量，这 p 种情形看作是单元内因子的p 个水平。这就是我们所考虑的多响应变量的情况。这一部分研究的MRM设计是单因子MRMA
2、NOV A，它只有一个试验单元内在因子。为方便起见，我们用“时间”来表示这个因子，而试验单元之间的因子，我们用“组”来表示。假定“组”这个因子有 q 个水平，在第 j 个水平有 n_j 个个体，j=1，2，q。n=n_1+n_q 就是整个样本容量的大小。对单因子MRM，我们考虑一个线性模型，其中的参数含有一个试验单元之间的随机效应。令 Y_(ijk)=Y_(ijk1)Y_(ijkr)。它是第 j 组中个体 i 在 k 时刻的测量值，试验单元之间的因子(组)j=1，q，i=1，n_j，试验单元内在因子(时间)k=1，p。在这个模型中，用一正交矩阵对观察值进行变换。我们感兴趣的问题是组效应，时间效
3、应，组和时间之间的交互效应的检验问题。基于变换后的第一组数据集做的ANOVA 作为试验单元之间组效应的ANOVA，而基于变换后的第k=2，p 组数据集做的 ANOVA 作为试验单元内在因子时间效应，以及组和时间之间的交互效应的ANOVA。论文中给出了所有的检验统计量，并对球形检验进行研究。论文得到了球形检验的似然比准则，它的渐近展开与极限分布。第二部分：考虑广义球形检验问题。论文得到了这个问题的检验准则，并给出了它的渐进展开。作为应用，我们研究了两个模型中的广义球形检验问题。第一个模型是套重复测量模型(NRMM)。在 NRMM 中，各独立个体中含有相同数目的子个体，每个子个体接受相同数目行处理
4、和列处理。我们假定所有的测量值都有相同的方差 2；来自同一个体但是不同子个体的两个测量值的协方差为 2_1；来自同一个体且是同一子个体的两个测量值，若列处理和行处理都不同，则其协方差为2_2；若列处理相同而行处理不同，则其协方差为2_3；若行处理相同而列处理不同，则其协方差为 2_4。第二个模型就是本文第一章主要研究的单因子重华东师范大学博士学位论文(2004 少复测量方差分析模型.对这两个模型都给出了似然比检验准则、渐进展开和极限分布.第三部分:考虑多变量线性模型 y、N(XB，艺因 V)，其中设计矩阵X 不一定是满秩，离差阵V 可以是奇异的。论文将艺的最小范数二次无偏估计(MINQUE)和
5、通常使用的最小二乘估计(LSE)进行比较。使用的损失函数有二次损失函数、嫡损失函数和对称损失函数。论文基于以下三个准则:二次损失风险准则、嫡损失风险准则和对称损失风险准则，将MINQUE 和 LSE 进行比较.在基于二次损失风险准则进行比较时，得到了 MINQUE 优于 LSE 的充分必要条件;在基于嫡损失风险准则进行文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1
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9、M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z
10、7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4
11、文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2
12、W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4比较时，证明了MINQUE 不比 LSE 差，并且得到了MINQUE 优于LSE 的充分必要条件;在基于对称损失风险准则进行比较时，得到了MINQUE 优于 LSE 的一些充分条件和必要条件。【关键词】：单因子多变量重复测量方差分析似然比准则球形检验渐进展开多变量线性模型套重复测量模型最小范数二次无偏估计风险函数二次损失函数熵损失函数对称损失函数【学位授予单位】：华东师范大学【学位级别】：博士【学位授予年份】：2004【分类号】：O29【目录】：AbstractinChinese5-7AbstractinEnglish7-10ACKNOW
13、LEDGMENTS10-11Chapter1INTRODUCTION11-331.1RepeatedMeasurementsDesigns11-191.2TestofCovarianceMatricesandSphericityTest19-261.3MINQUEandOrdinaryLeastSquaresEstimator26-301.4MainWorkinthisThesis30-33Chapter2One-wayMRMANOV AModel33-562.1Introduction332.2One-wayMRMDesigns33-362.3AnalysisofVariance(ANOVA
14、)36-432.4TheSphericityTest43-502.5AsymptoticExpansionofSphericityTest50-532.6Examples53-56Chapter3GeneralizedSphericityTest56-733.1Introduction563.2TheCrite文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8
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20、:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1
21、 HA8B4D7M5Z7 ZY6R7O1F1Z4rion56-643.3AsymptoticExpansionofGeneralizedSphericityTest64-663.4SphericityTestinNestedRepeatedMeasuresModel66-703.5SphericityTestinOne-wayMRMANOV AModel70-73Chapter4ComparisonofMINQUEandSimpleEstimator73-974.1Introduction734.2MultivariateLinearModelandLossFunctions73-744.3C
22、omparisonofEstimators74-97Appendix197-100Bibliography100-108ResearchWork108-109 本论文购买请联系页眉网站。文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档编码:CP10S5P2W8M1 HA8B4D7M5Z7 ZY6R7O1F1Z4文档
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