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

Abstract

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.