In this paper, we mainly study the Berry–Esseen type bounds of wavelet estimator in a semiparametric model Yi = xiβ + g(ti) + εi, 1 ⩽ i ⩽ n, where the linear process εi = \({\sum }_{j=-\infty }^{\infty }{a}_{j}{e}_{i-j}\) with \({\sum }_{j=-\infty }^{\infty }\left|{a}_{j}\right|<\infty ,\) and ei are asymptotically negatively associated (ANA or ρ–, for short) random variables. Under appropriate conditions, the Berry–Esseen-type bounds for estimators of β and g(·) can attain nearly O(n−1/4) and O(n−1/8), respectively. The results obtained in this paper significantly improve and extend the corresponding results for negatively associated random variables and other mixing random variables. Numerical simulations are used to more specifically show the effectiveness of the method and the validity of the theoretical results.
