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

被引：22

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.

引用

页码：503 / 518

页数：16

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