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In the paper, the central limit theorem for asymptotically negatively associated (ANA, for short) random variables is established. As an application, we consider the nonparametric regression model with repeated measurements:, whereis the  j th response at the point,'s are known fixed design points, andis an unknown Borel measurable function defined on. Under some general conditions, we study the asymptotic normality of the wavelet estimator ofunder ANA random errors. The obtained results generalize the corresponding ones for NA random variables. Finally, we will provide the simulation study to assess the finite sample performance of the theoretical results.

The central limit theorem for ANA sequences and its application to nonparametric regression models