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

• Published in: Journal of mathematical analysis and applications Vol. 494; no. 2; p. 124566
• Main Authors: Wu, Yi, Wang, Xuejun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2021
• Subjects: Complete convergence; Conditional Value-at-risk estimator; m-extended negatively dependent random variables; Multiple linear regression model; Quasi-renewal counting process; Strong consistency; Conditional Value-at-risk estimator; m-extended negatively dependent random variables; Complete convergence; Strong consistency; Multiple linear regression model; Quasi-renewal counting process
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2020.124566

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.