Some convergence properties for arrays of rowwise asymptotically almost negatively associated random variables under sub-linear expectations

• Published in: Stochastic models Vol. 40; no. 3; pp. 536 - 568
• Main Authors: Wang, Miaomiao, Zheng, Shunping, Wang, Xuejun
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02-07-2024; Taylor & Francis Ltd
• Subjects: Arrays; Asymptotically almost negatively associated random variables; capacity; complete moment convergence; Consistency; Convergence; Errors; Numerical models; Random variables; Regression models; Statistical analysis; sub-linear expectation space
• ISSN: 1532-6349; 1532-4214
• DOI: 10.1080/15326349.2023.2286961

In this article, under some suitable conditions, we study the L
q
convergence and complete q-th moment convergence for arrays of rowwise asymptotically almost negatively associated (AANA, for short) random variables under sub-linear expectations. Some general results on L
q
convergence and complete q-th moment convergence for arrays of rowwise AANA random variables under sub-linear expectations are established, which extend the corresponding ones from classic probability space to the case of sub-linear expectation space. As applications of our main results, we not only present a result on the complete consistency of the weighted estimator in a nonparametric regression model but also obtain the complete consistency of the estimators in errors-in-variables (EV, for short) regression models based on AANA errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results.