Strong laws for weighted sums of m-extended negatively dependent random variables and its applications

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.