Abstract In this paper, the sufficient and necessary conditions for complete convergence and the Kolmogorov strong law of large numbers for weighted sums of m-extended negatively dependent random variables are presented. Some applications of the main results are also provided, including the weak and strong consistency of the least squares estimator in multiple linear regression models, strong consistency of conditional Value-at-risk estimator, and the asymptotics of the quasi-renewal counting process. Finally, some numerical simulations are carried out to confirm the theoretical results.

中文翻译：

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m-扩展负相关随机变量加权和的强定律及其应用

摘要 本文给出了m-扩展负相关随机变量的加权和的完全收敛的充要条件和Kolmogorov强数定律。还提供了主要结果的一些应用，包括多元线性回归模型中最小二乘估计量的弱一致性和强一致性，条件风险价值估计量的强一致性，以及准更新计数过程的渐近性。最后，进行了一些数值模拟以验证理论结果。