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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.

Weak convergence for weighted sums of negatively associated random variables and its application in nonparametric regression models