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

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  • Jinyu Zhou
  • Jigao Yan
  • Dongya Cheng

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.

Suggested Citation

  • Jinyu Zhou & Jigao Yan & Dongya Cheng, 2023. "Complete convergence for maximum of weighted sums of WNOD random variables and its application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(22), pages 8184-8206, November.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:22:p:8184-8206
    DOI: 10.1080/03610926.2022.2059681
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