Strong laws for weighted sums of widely orthant dependent random variables and applications

IF 1 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2024-08-26 DOI:10.1515/math-2024-0027

Yong Zhu, Wei Wang, Kan Chen

引用次数: 0

Abstract

In this study, the strong law of large numbers and the convergence rate for weighted sums of non-identically distributed widely orthant dependent random variables are established. As applications, the strong consistency for weighted estimator in nonparametric regression model and the rate of strong consistency for least-squares estimator in multiple linear regression model are obtained. Some numerical simulations are also provided to verify the validity of the theoretical results.

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广泛正交依存随机变量加权和的强定律及其应用

本研究建立了非同分布广泛正交因变量加权和的强大数定律和收敛速率。作为应用，研究还获得了非参数回归模型中加权估计器的强一致性和多元线性回归模型中最小二乘估计器的强一致性率。此外，还提供了一些数值模拟来验证理论结果的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: