Theoretical analysis demonstrates complete convergence for weighted sums in extended negatively dependent random variables, suggesting broad consistency for nonparametric regression estimators.
In this paper, complete convergence and complete moment convergence for maximal weighted sums and product sums of arrays of rowwise mn-extended negatively dependent random variables are investigated, and some sufficient conditions for convergence are provided. A discussion of how the moment condition can be reduced in the Baum-Katz type theorem with certain weight condition is given. Besides, rather than assuming stochastic domination, we turn to a weaker assumption of uniformly bounded expectations to describe the moment conditions. Additionally, a Marcinkiewicz–Zygmund type strong law of large numbers for product sums of widely orthant dependent random variables is established. The results obtained in the paper extend the corresponding ones for independent and some dependent structures. In addition, the results are applied to establishing strong consistency for estimators in nonparametric regression model and statistics in bootstrap.
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Zhou et al. (2026) studied this question.