A Berry-Esseen Type Bound of Wavelet Estimator Under Linear Process Errors Based on a Strong Mixing Sequence
Consider the nonparametric regression model Y ni = g(t ni ) + ϵ ni , 1 ≤ i ≤ n, where {t ni } are known design points, and the errors {ϵ ni } have a linear representation with and {e t , − ∞ <t < ∞} are strong mixing random variables. g(·) is an unknown function defined on closed interval [0,1], which is estimated by a linear wavelet estimator . The main result of this article is that of providing, under certain regularity conditions, a Berry-Esseen boundary for the linear wavelet estimator , and the Berry-Esseen bound can attain O(n −1/6).