Complete convergence for maximum of weighted sums of WNOD random variables and its application

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 52; no. 22; pp. 8184 - 8206
Main Authors Zhou, Jinyu, Yan, Jigao, Cheng, Dongya
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 17.11.2023
Taylor & Francis Ltd
Subjects
Complete convergence
Convergence
Dependent variables
maximum of weighted sums
Random variables
Regression models
strong law of large numbers
widely negative orthant dependent
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Summary:In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2022.2059681