Robustness of F-Tests in Singular Linear Models

作     者：Hong Bing QIU Ji LUO Jia Jia ZHANG 

作者机构：School of Applied Mathematics Guangdong University of Technology School of Mathematics and Statistics Zhejiang University of Finance and Economics Department of Epidemiology and Biostatistics University of South Carolina 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第5期

页      面：872-880页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Social Science Foundation of China(Grant No.13CTJ012) National Natural Science Foundation of China(Grant No.11171058) Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ13A010002) Guangdong Provincial Natural Science Foundation of China(Grant No.S2012040007622) he National Statistical Science Research Project(Grant No.2012LY129) 

主　　题：Linear model F-test robustness maximal class 

摘      要：F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of robust F-test statistic are given under the general linear models or their partition models, which allows that the design matrix has deficient rank and the covariance matrix of error is a nonnegative definite matrix with parameters. The main results obtained in this paper include the existing findings of the general linear model under the definite covariance matrix. The usage of the theorems is illustrated by an example.