Abstract
In this work, a generalised concept of dependent random variables, i.e., m-widely acceptable random variables, is put forward and some inequalities such as exponential inequality and Rosenthal-type inequality are established under sub-linear expectations. By virtue of these inequalities, we obtain a general result on complete convergence and the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of m-widely acceptable random variables, which extend and improve some existing ones in classical probability space as well as in sub-linear expectation space. As applications of the main results, the complete consistency and strong consistency of weighted estimators in nonparametric regression model under sub-linear expectations are also investigated.
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