Complete convergence for randomly weighted sums of dependent random variables and an application

Pingyan Chen, Jingjing Luo and Soo Hak Sung

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 20, 7197-7215

Abstract: In this article, we establish complete convergence for randomly weighted sums of negatively orthant-dependent random variables. We also establish complete convergence for the maximums of randomly weighted sums of negatively associated random variables. As a corollary, a Marcinkiewicz-Zygmund-type strong law for randomly weighted sums of negatively associated random variables is obtained. The results can be applied to the bootstrap sample means, and an open problem in a convergence rate of the bootstrap sample means posed by Csörgő (2004) is solved completely.

Date: 2024
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DOI: 10.1080/03610926.2023.2262636

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