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Gauss-Markov估计关于误差分布的稳健性 被引量：5

Robustness of Gauss-Markov Estimator in Terms of Error Distributions
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摘要 对于一般线性模型y=Xβ+ε,本文讨论了在广义均方误差准则及均方误差矩阵准则下,未知参数β的可估函数Xβ的Gauss-Markov估计关于误差分布的稳健性,分别给出了误差项ε的最大分布类,使得误差项ε的分布在此范围内变动时,Gauss-Markov估计在相应准则下是最优估计. Robustness of Gauss-Markov estimator of estimable function of unknown parameter in terms of error distributions is discussed in general linear model. We explore the maximal distribution classes of error term, where Gauss-Markov estimator held its optimality by generalized mean squared errors criterion and by mean square error matrix criterion respectively.
作者 邱红兵 罗季
机构地区 广东工业大学应用数学学院 浙江财经学院数学与统计学院
出处 《应用概率统计》 CSCD 北大核心 2010年第6期615-622,共8页 Chinese Journal of Applied Probability and Statistics
基金 国家社会科学基金项目(07CTJ001) 国家自然科学基金项目(10871168) 广东工业大学校青年基金项目(082024)资助
关键词 线性模型 广义均方误差 均方误差矩阵 Gauss-Markov估计 Linear model generalized mean squared errors mean square error matrix Gauss-Markov estimator.
分类号 O212 [理学—概率论与数理统计]
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参考文献9

  • 1Rao, C.R., Linear Statistical Inference and Its Applications, 2nd ed, Wiley, New York, 1973.
  • 2Kariya, T. and Kurata, H., A maximal extension of the Gauss-Markov theorem and its nonlinear version, Y. Multivariate Anal., 83(2002), 37-55.
  • 3刘湘蓉.最小二乘估计关于误差分布的稳健性[J].应用概率统计,2006,22(4):429-437. 被引量：8
  • 4Rao, C.R. and Mitra, S.K., Generalized Iverse of Matrices and Its Applications, Wiley, New York, 1971.
  • 5Mathew, T. and Bhimasankaram, P., Optimality of BLUE's in a genral linear model with incorrect design matrix, J. Statist. Plan. Infer., 8(1983), 315 369.
  • 6Ali, M.M. and Ponnapalli, R., An optimality of the Gauss-Markov estimator, .]. Multivariate Anal., 32(1990), 171-176.
  • 7Puntanen, S., Some matrix results related to reduced singular linear model, Comm. Statist. A -- Theory Methods, 25(2)(1996), 269-279.
  • 8Puntanen, S., Some further results related to reduced singular linear models, Comm. Statist., 26(2)(1997), 375-385.
  • 9Werner, H.J. and Yapar, C., A BLUE decomposition in the general linear regression model, Linear Algebra Appl., 237/238(1996), 395-404.

二级参考文献5

  • 1Eaton, M.L., Concentration inequalities for Gauss-Markov estimator, J. Multivariate Anal., 25(1988),119-138.
  • 2Berk, R. and Hwang, J.T., Optimality of the least squares estimator, J. Multivariate Anal., 30(1989),245-254.
  • 3Rao, C.R. and Mitra, S.K., Generalized Inverse of Matrices and Its Applications, Wiley, New York,1971.
  • 4Kariya, T. and Kurata, H., A maximal extension of the Gauss-Markov theorem and its nonlinear version, J. Multivariate Anal., (83)(2002), 37-55.
  • 5Ali, M.M. and Ponnapalli, R., An optimality of the Gauss-Markov estimator, J. Multivariate Anal.,32(1990), 171-176.

共引文献7

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应用概率统计
2010年 第6期

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