| 线性模型下F-检验最优的误差协方差结构 |
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| 引用本文： | 吴密霞,王松桂.线性模型下F-检验最优的误差协方差结构[J].数学学报,2006,49(3):595-604. |
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| 作者姓名： | 吴密霞 王松桂 |
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| 作者单位： | 北京工业大学应用数理学院,北京100022 |
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| 基金项目： | 国家自然科学基金资助项目（10271010）;北京市自然科学基金资助项目（1032001） |
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| 摘 要： | 文献中回归参数线性假设的F-检验统计量主要包括基于广义最小二乘估计F- 统计量F(θ),基于最小二乘估计的F-统计量FLSE以及Wu C．F．J．等于1988年提出的调整的F-统计量FA(θ)．其中后两者因形式简单而常常被广泛采用．本文主要研究了FA(θ)和FLSE的最优性,并分别获得了FA(θ)=F(θ)和ELSE=F(θ)的充要条件．最后,我们将所得的结果应用到医药领域的两类重要模型．
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| 关 键 词： | 最小二乘估计 一致最优功效无偏检验 F检验 |
| 文章编号： | 0583-1431（2006）03-0595-10 |
| 收稿时间： | 2004-11-22 |
| 修稿时间： | 2004-11-222005-03-29 |
Optimal Structure of the Covariance Matrix of Errors for F-Tests in Linear Models |
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| Mi Xia WU Song Gui WANG.Optimal Structure of the Covariance Matrix of Errors for F-Tests in Linear Models[J].Acta Mathematica Sinica,2006,49(3):595-604. |
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| Authors: | Mi Xia WU Song Gui WANG |
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| Institution: | College of Applied Sciences, Beijing University of Technology, Beijing 100022, P. R. China |
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| Abstract: | In the literature, F-statistics used in testing linear restrictions mainly include F(θ) based on the general least squares estimate, FLSE based on the least squares estimate, and the adjusted F-statistic FA(θ) given by C. F. J. Wu, et al. in 1988. Due to their simple forms, the latter two are more commonly employed in practice. In this paper, we mainly consider the optimality of FA(θ) and FLSE, and obtain the necessary and sufficient conditions for FA(θ)=F(θ) and FLSE=F(θ), respectively. Lastly, we apply the results obtained to two important models in the field of pharmacology. |
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| Keywords: | least squares estimate uniformly most powerful unbiased test F-test |
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