A Berry-Esseen Type Bound of Wavelet Estimator Under Linear Process Errors Based on a Strong Mixing Sequence

摘要

Consider the nonparametric regression model Y_(ni) = g(t_(ni)) + ε_(ni), I ≤i≤ n, where {t_(ni)} are known design points, and the errors {ε_(ni)} have a linear representation ε_(ni) = Σ_(j=-∞)~∞ a_je_(i-j) with Σ_(i=-∞)~∞|a_i| ＜ ∞ 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 g_n(t). The main result of this article is that of providing, under certain regularity conditions, a Berry-Esseen boundary for the linear wavelet estimator g_n(t), and the Berry-Esseen bound can attain O(n~(-1/6).