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In this article, under some suitable conditions, we study the Lq 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 Lq 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. [ABSTRACT FROM AUTHOR]

In this paper, the complete f-moment convergence for weighted sums of sequences of extended negatively dependent random variables is investigated. As a result, we not only extend and generalize some results on complete convergence obtained by Wu and Zhai (Journal of Mathematical Inequalities, 13(1): 251-260, 2019), but also get some results on the complete consistency for the estimator of nonparametric regression models and provide some simulations to assess the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we investigate some convergence properties, such as complete convergence, complete moment convergence, complete f-moment convergence and strong law of large numbers, for partial sums of randomly weighted sums of ρ-mixing sequences by using the moment inequality, which extend and improve the corresponding ones in the literature. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression models and the estimators for the unknown parameters in the simple linear errors-in-variables regression models based on ρ-mixing errors. [ABSTRACT FROM AUTHOR]

In this paper, we study the weak convergence and convergence rate in the weak law of large numbers for weighted sums of a class of random variables satisfying the Rosenthal type inequality. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers under some mild conditions are provided. Moreover, the main results that we established are applied to simple linear errors-in-variables regression models and nonparametric regression models based on a class of random errors. Finally, we present some numerical simulations to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the complete convergence and complete moment convergence for randomly weighted sums of arrays of rowwise widely negative dependent random variables in sub-linear expectation space under some appropriate conditions, which extend and improve the corresponding ones in classical probability space to the case of sub-linear expectation space. And we obtain a strong law of large numbers for the randomly weighted sums of arrays of rowwise widely negative dependent random variables. As applications of our main results, we not only present a result on the complete consistency for the weighted estimator in a nonparametric regression model, but also obtain the complete consistency for the least squares estimators in errors-in-variables regression models based on widely negative dependent errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results and a real example is analysed for illustration. [ABSTRACT FROM AUTHOR]