A Berry-Ess$\acute{e}$n bound of wavelet estimation for a nonparametric regression model under linear process errors based on LNQD sequence

Abstract

By using some inequalities for linearly negative quadrant dependent random variables, Berry-Ess$\acute{e}$en bound of wavelet estimation for a nonparametric regression model is investigated under linear process errors based on linearly negative quadrant dependent sequence. The rate of uniform asymptotic normality is presented and the rate of convergence is near $O(n^{-\frac{1}{6}})$ under mild conditions, which generalizes or extends the corresponding results of Li et al.(2008) under associated random samples in some sense.