线性模型中F-检验的稳健性

邱红兵, 罗季

数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 385-392.

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数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 385-392. DOI: 10.12386/A2010sxxb0045
论文

线性模型中F-检验的稳健性

    邱红兵1, 罗季2
作者信息 +

Robustness of F-test in Linear Models

    Hong Bing QIU1, Ji LUO2
Author information +
文章历史 +

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.

 

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.

 

关键词

线性模型 / 稳健性 / F-检验统计量

Key words

linear model / robustness / F-statistics

引用本文

导出引用
邱红兵, 罗季. 线性模型中F-检验的稳健性. 数学学报, 2010, 53(2): 385-392 https://doi.org/10.12386/A2010sxxb0045
Hong Bing QIU, Ji LUO. Robustness of F-test in Linear Models. Acta Mathematica Sinica, Chinese Series, 2010, 53(2): 385-392 https://doi.org/10.12386/A2010sxxb0045

参考文献


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基金

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)及浙江财经学院重大课题(2008YJZ06)

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