Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications

被引：13
|
作者：
Shen, Aiting [1 ]
Volodin, Andrei [2 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China
[2] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada
来源：
METRIKA | 2017年 / 80卷 / 6-8期
基金：
中国国家自然科学基金;
关键词：
Extended negatively dependent random variables; Lr convergence; Marcinkiewicz-Zygmund type moment inequality; Law of large numbers; Nonparametric regression models; DEPENDENT RANDOM-VARIABLES; PRECISE LARGE DEVIATIONS; FIXED-DESIGN REGRESSION; COMPLETE CONVERGENCE; WEIGHTED SUMS; INEQUALITIES; THEOREMS;
D O I：
10.1007/s00184-017-0618-z
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 the paper, the Marcinkiewicz-Zygmund type moment inequality for extended negatively dependent (END, in short) random variables is established. Under some suitable conditions of uniform integrability, the convergence, weak law of large numbers and strong law of large numbers for usual normed sums and weighted sums of arrays of rowwise END random variables are investigated by using the Marcinkiewicz-Zygmund type moment inequality. In addition, some applications of the convergence, weak and strong laws of large numbers to nonparametric regression models based on END errors are provided. The results obtained in the paper generalize or improve some corresponding ones for negatively associated random variables and negatively orthant dependent random variables.
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页码：605 / 625
页数：21
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