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

Jinyu Zhou, Jigao Yan and Dongya Cheng

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 22, 8184-8206

Abstract: 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.

Date: 2023
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DOI: 10.1080/03610926.2022.2059681

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