Hong Chang HU School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,P.R.China
Consider the semiparametric regression model y_i=X_i~Tβ+g(t_i)+ε_i(i= 1,...,n),where random errors{ε_i,i=1,...,n}are stationary and long range dependence (LRD) stochastic processes,and Xi is a vector of random design points.Under this case,the wavelet estimators of both parameters and nonparameters are attained, and consistency and convergence rates in probability are investigated under some mild conditions.Our results generalize some corresponding results in the model with independent random errors.