An Almost Sure Central Limit Theorem for Self-normalized Weighted Sums

作     者：Yong ZHANG Xiao-yun YANG 

作者机构：College of Mathematics Jilin University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2013年第29卷第1期

页      面：79-92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 the National Natural Science Foundation of China (No. 10971081  11101180) 

主　　题：almost sure central limit theorem self-normalized weighted sums domain of attractio of thenormal law 

摘      要：Let X, X1, X2, be a sequence of nondegenerate i.i.d, random variables with zero means, which is in the domain of attraction of the normal law. Let （ani, 1 ≤ i ≤n,n ≥1} be an array of real numbers with some suitable conditions. In this paper, we show that a central limit theorem for self-normalized weighted sums holds. We also deduce a version of ASCLT for self-normalized weighted sums.