The Berry-Esseen bounds of wavelet estimator for nonparametric regression models whose errors form a linear process based on ANA sequences

In this paper, we consider the nonparametric regression model $ Y_{ni}= g(t_{ni})+\varepsilon _i $ Yni=g(tni)+& varepsilon;i ( $ 1\leq i\leq n $ 1 <= i <= n), where $ \varepsilon _{i}=\sum _{j=-\infty }<^>{\infty }a_je_{i-j} $ & varepsilon;i=& sum;j=-infinity infinity ajei-j and $ e_{i} $ ei are identically distributed and asymptotically negatively associated (ANA or $ \rho <^>- $ rho-, for short) sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of $ g(\cdot ) $ g(& sdot;), and the rate of the normal approximation is shown as $ O(n<^>{-1/4}) $ O(n-1/4) under certain conditions. Finally, the simulation study is provided to verify the validity of the theoretical results.