The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors

Abstract

Consider the nonparametric regression model Y ni = g (t ni ) + e i , i = 1, 2, …, n ,  n ≥ 1, where e i ,  1 ≤ i ≤ n , are asymptotically negatively associated (ANA, for short) random variables. Under some appropriate conditions, the Berry-Esseen bound of the wavelet estimator of g (⋅) is established. In addition, some numerical simulations are provided in this paper. The results obtained in this paper generalize some corresponding ones in the literature.