| 约束条件下线性模型协方差阵扰动的影响分析 |
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| 引用本文： | 张尚立,覃红.约束条件下线性模型协方差阵扰动的影响分析[J].数学物理学报(A辑),2006,26(4):621-628. |
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| 作者姓名： | 张尚立 覃红 |
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| 作者单位： | 北京交通大学数学系，华中师范大学数学与统计学学院 北京 100044，武汉 430079 |
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| 基金项目： | 国家重大基础研究前期研究专项基金(2003CCA02400)，教育部留学回国人员科研启动基金([2004]176)，湖北省自然科学基金(2003ABA022)资助 |
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| 摘 要： | 该文研究了协方差阵扰动和数据删除对最佳线性无偏估计(BLUE)的影响问题, 给出了在约束条件下一般线性模型与在约束条件下Gauss-Markov模型及在约束条件下数据删除模型中回归参数β的BLUE之间的关系式. 作者还定义了度量影响大小的广义Cook距离DV并给出了DV的两个计算公式.
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| 关 键 词： | 一般线性回归模型 约束条件 最佳线性无偏估计 影响分析 |
| 文章编号： | 1003-3998(2006)04-621-08 |
| 收稿时间： | 2004-12-14 |
| 修稿时间： | 2006-02-16 |
Influence Analysis of Covariance Matrix Disturbance in Linear Model with Respect to a Restricted Condition |
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| Zhang Shangli,Qin Hong.Influence Analysis of Covariance Matrix Disturbance in Linear Model with Respect to a Restricted Condition[J].Acta Mathematica Scientia,2006,26(4):621-628. |
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| Authors: | Zhang Shangli Qin Hong |
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| Institution: | 1.Department of Mathematics, Beijing Jiaotong University, Beijing 100044;2.Department of Statistics, Centeral China Normal University, Wuhan 430079 |
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| Abstract: | In this paper, the authors study the issue of the influence of Best Linear Unbiased Estimate (BLUE) with covariance matrix disturbingor data missing. The relationship of the BLUE of regression parameter β among some linear models with respect to restricted condition β=0, such as Gauss-Markov model, generalized linear model and linear model with delected data, is made explicitly. In addition, the authors also propose the generalized Cook distance DV to asses the disturbing influence, and obtain two computational formulae of DV. |
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| Keywords: | Generalized linear regression model Restricted condition Best linear unbiased estimate Influence analysis |
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