Uniform integrability of the OLS estimators, and the convergence of their moments

作     者：Afendras, Georgios Markatou, Marianthi 

作者机构：SUNY Buffalo Dept Biostat 811 Kimball Tower Buffalo NY 14214 USA SUNY Buffalo Jacobs Sch Med & Biomed Sci 811 Kimball Tower Buffalo NY 14214 USA SUNY Buffalo Dept Biostat 726 Kimball Tower Buffalo NY 14214 USA SUNY Buffalo Jacobs Sch Med & Biomed Sci 726 Kimball Tower Buffalo NY 14214 USA 

出 版 物：《TEST》 (验算：西班牙统计与运筹学会杂志)

年 卷 期：2016年第25卷第4期

页      面：775-784页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：Department of Biostatistics Jacobs School of Medicine and Biomedical Sciences, University at Buffalo 

主　　题：Linear regression model Moment convergence Rate of convergence Uniform integrability 

摘      要：The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross-validation estimation of the generalization error of computer algorithms, and in the construction of graphical methods for studying dependence patterns between two biomarkers. In this paper, we prove the uniform integrability of the ordinary least squares estimators of a linear regression model, under suitable assumptions on the design matrix and the moments of the errors. Further, we prove the convergence of the moments of the estimators to the corresponding moments of their asymptotic distribution, and study the rate of the moment convergence. The canonical central limit theorem corresponds to the simplest linear regression model. We investigate the rate of the moment convergence in canonical central limit theorem proving a sharp improvement of von Bahr s (Ann Math Stat 36:808-818, 1965) theorem.