In this paper, we establish a general result on complete moment convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for weighted sums of m-asymptotic negatively associated random variables, which improve and extend some existing ones. As applications of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model and a result on strong consistency for conditional Value-at-risk estimator based on m-asymptotic negatively associated errors. We also carry out some numerical simulations to confirm the theoretical results.

中文翻译：

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m-渐近负相关随机变量和统计应用的加权和的强收敛特性

在本文中，我们建立了关于 m 渐近负相关随机变量的加权和的完全矩收敛的一般结果和 Marcinkiewicz-Zygmund 型强数定律，改进和扩展了一些现有的。作为我们主要结果的应用，我们提出了非参数回归模型中加权估计量的完全一致性结果和基于 m 渐近负相关误差的条件风险价值估计量的强一致性结果。我们还进行了一些数值模拟来验证理论结果。