Strong Convergence for Weighted Sums of Negatively Associated Arrays

作     者：Hanying LIANG Jingjing ZHANG Hanying LIANG Jingjing ZHANG Department of Mathematics,Tongji University,Shanghai 200092,China

作者机构：Department of Mathematics Tongji University Shanghai 200092 China. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2010年第31卷第2期

页      面：273-288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] 081401[工学-岩土工程] 08[工学] 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] 0814[工学-土木工程] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (No.10871146) the Spanish Ministry of Science and Innovation (No.MTM2008-03129) the Xunta de Galicia,Spain (No.PGIDIT07PXIB300191PR) 

主　　题：Tail probability Negatively associated random variable Weighted sum 

摘      要：Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑｜i｜≤k Ф（i/nη）1/nη Xni for η∈（0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP（max 1≤k≤n｜Tnk｜〉εBn）〈∞ and ∞∑n=1 CnP（max 0≤k≤mn｜Snk｜〉εDn）〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented.