Asymptotic normality of wavelet estimators in heteroscedastic regression model with ANA errors

In this article, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with asymptotically negatively associated (ANA or ρ−, for short) errors. Under some mild conditions, the asymptotic normality of the wavelet estimators of g(⋅) in the heteroscedastic regression model with ANA errors is obtained when f(⋅) is a known or unknown function, respectively. At the same time, we derive a Berry-Esseen-type bound for the estimators of g(⋅). As a corollary, by making a certain choice of the weights, the Berry-Esseen-type bound of the estimator can reach nearly O(n−1/12), which in some sense generalizes or improves the corresponding ones for negatively associated (NA, for short) random variables and φ−mixing sequence. Finally, the finite sample simulation study presented in this article shows the validity of our theoretical results.