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In this article, the complete moment convergence for randomly weighted sums of negatively superadditive dependent (NSD, for short) random variables is studied. Several sufficient conditions of the complete moment convergence for randomly weighted sums of NSD random variables are presented. The results obtained in the article extend some corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generalize the corresponding ones of [M.M. Xi, X. Deng, X.J. Wang, and Z.Y. Cheng, L p convergence and complete convergence for weighted sums of AANA random variables, Commun. Stat. Theory Methods 47(22) (2018), pp. 5604–5613]. As an application of our main results, some results on the complete consistency for the estimator in semiparametric regression models are obtained and a simulation study is provided to assess the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the weak convergence and convergence rates in the weak law of large numbers for weighted sums of negatively associated random variables. The necessary and sufficient conditions for the convergence rates in the weak law of large numbers are provided. As an application, the weak consistency for the weighted linear estimator of nonparametric regression models is established. Some numerical simulations are also provided to verify the validity of the theoretical result. [ABSTRACT FROM AUTHOR]