| 线性模型中F-检验的稳健性 |
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| 引用本文： | 邱红兵,罗季.线性模型中F-检验的稳健性[J].数学学报,2010,53(2):385-392. |
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| 作者姓名： | 邱红兵 罗季 |
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| 作者单位： | 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; |
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| 基金项目： | 国家社会科学基金项目(07CTJ001); 广东工业大学校青年基金项目(082024); 浙江省教育厅科研项目(Y200802985); 浙江财经学院重大课题(2008YJZ06) |
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| 摘 要： | 本文讨论了一般线性模型中关于均值参数β的线性假设基于广义最小二乘估计的F-检验统计量的稳健性问题.主要研究了当误差的协方差矩阵含有参数时,设计阵可以列降秩情况下的F-检验统计量的稳健性,得到了F(V(θ))为该假设下F-检验统计量的误差协方差矩阵的最大类.并讨论了分块线性模型中,关于分块参数的线性假设的F-检验统计量的稳健性.
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| 关 键 词： | 线性模型 稳健性 F-检验统计量 |
| 收稿时间： | 2009-02-09 |
| 修稿时间： | 2009-10-27 |
Robustness of F-test in Linear Models |
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| Hong Bing QIU Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou ,P.R.China Ji LUO School of Mathematics , Statistics,Zhejiang University of Finance , Economics,Hangzhou ,P.R.China.Robustness of F-test in Linear Models[J].Acta Mathematica Sinica,2010,53(2):385-392. |
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| Authors: | Hong Bing QIU Faculty of Applied Mathematics Guangdong University of Technology Guangzhou PRChina Ji LUO School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou PRChina |
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| Institution: | Hong Bing QIU Faculty of Applied Mathematics,Guangdong University of Technology,Guangzhou 510006,P.R.China Ji LUO School of Mathematics , Statistics,Zhejiang University of Finance , Economics,Hangzhou 310018,P.R.China |
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| Abstract: | Robustness of F-test based on the general least squares estimate used in testing linear restrictions is discussed in general linear model. We mainly study robustness of the F-statistics in the cases of variance matrix of error including parameter and design matrix with reduced-rank columns. The maximal classes of variance matrix of error are derived, in which F(V(θ)) is F-statistics of the linear restriction. Also the robustness of F-statistics with respect to linear restrictions for partitioned parameters in partitioned linear model is considered.
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| Keywords: | linear model robustness F-statistics |
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