Complete moment convergence for double-indexed randomly weighted sums and its applications

被引：21
|
作者：
Wang, Xuejun [1 ]
Wu, Yi [1 ]
Hu, Shuhe [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei, Anhui, Peoples R China
来源：
STATISTICS | 2018年 / 52卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Complete moment convergence; complete convergence; randomly weighted sums; nonparametric regression model; state observers; linear-time-invariant systems; NSD RANDOM-VARIABLES; DEPENDENT RANDOM-VARIABLES; FIXED-DESIGN REGRESSION; NONPARAMETRIC REGRESSION; MAXIMAL INEQUALITIES; MIXING SEQUENCES; QUADRATIC-FORMS; TIME-SERIES; ASSOCIATION; ARRAYS;
D O I：
10.1080/02331888.2018.1436548
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：
In this paper, we mainly study the complete moment convergence of double-indexed randomly weighted sums of negatively superadditive-dependent (NSD, for short) random variables, which is stronger than complete convergence. In addition, the convergence of double-indexed randomly weighted sums of NSD random variables is also obtained. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors, and study the almost sure convergence and mean square convergence of the state observers of linear-time-invariant systems.
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页码：503 / 518
页数：16
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