USE THE METHODS OF CV AND GCV TO ESTIMATE NONPARAMETRIC REGRESSION FUNCTIONS

Suppose nonparametric regression model to be y_i=f（x₄）+ε_i,i=1,…,n.f（x） is an unknown nonparametric regression function on 0,1. The kernel estimator of f（x） has a smoothing parameter h. Use (CV and GCV criterions to choose the smoothing parameter hrespeetively, an optimal nonparametric kernel estimator is obtained. Assume ε_i to be i. i. d. r. v. s., under the condition that the fourth moment of ε_i is finite, the chosen kernel estimators and the associated Stein’s estimators are consistent.