Strong convergence properties for weighted sums of WNOD random variables and its applications in nonparametric regression models

被引：5
|
作者：
Shen, Aiting [1 ]
Li, Xiang [1 ]
Ning, Mingming [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei, Peoples R China
来源：
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2021年 / 93卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Widely negative orthant dependent random variables; complete convergence; nonparametric regression model; complete consistency; DEPENDENT RANDOM-VARIABLES; COMPLETE MOMENT CONVERGENCE; ARRAYS;
D O I：
10.1080/17442508.2020.1734005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, the complete convergence for the maximum of weighted sums of widely negative orthant dependent (WNOD, in short) random variables is investigated under some suitable moment conditions. Some sufficient conditions to prove the complete convergence are provided. The results obtained in the paper generalize some corresponding ones for some dependent random variables. As an application, the complete consistency for the weighted estimator in a nonparametric regression model is established. Finally, we present some simulations to show the consistency for the nearest neighbour weight function estimator in a nonparametric regression model.
引用
收藏
页码：376 / 401
页数：26
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