Asymptotic results for random sums of dependent random variables

被引：11
|
作者：
Islak, Umit [1 ]
机构：
[1] Georgia Inst Technol, Sch Math, Dept Math, Atlanta, GA 30332 USA
来源：
STATISTICS & PROBABILITY LETTERS | 2016年 / 109卷
关键词：
Stein's method; Random sums; Central limit theorem; Concentration inequality; Local dependence; CENTRAL-LIMIT-THEOREM; NORMAL APPROXIMATION;
D O I：
10.1016/j.sp1.2015.10.015
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Our main result is a central limit theorem for random sums of the form Xi, where {X-i}i >= 1 is a stationary m-dependent process and N-n is a random index independent of {X-i}i >= 1. This extends the work of Chen and Shao on the i.i.d. case to a dependent setting and provides a variation of a recent result of Shang on m-dependent sequences. Further, a weak law of large numbers is proven for Sigma(Nn)(i=1) X-i, and the results are exemplified with applications on moving average and descent processes. (c) 2015 Elsevier B.V. All rights reserved.
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页码：22 / 29
页数：8
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