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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 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]