Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications

作     者：YUAN DeMei AN Jun 

作者机构：School of Mathematics and StatisticsChongqing Technology and Business UniversityChongqing 400067China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第9期

页      面：1887-1904页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 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）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.10871217) the SCR of Chongqing Municipal Education Commission (Grant No.KJ090703) 

主　　题：Rosenthal type inequality asymptotically almost negative association residual Cesàro α-integrability strong residual Cesàro α-integrability L p-convergence complete convergence Marcinkiewicz-Zygmund strong law 60F05 60F15 

摘      要：In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 p 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.