用CV和GCV方法估计非参数回归函数

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

设非参数回归模型为y_i=f(x_4)+ε_i,i=1,…,n,f(x)是[0,1]上未知的非参数回归函数。f(x)的核估计具有一个光滑参数h,分别利用CV和GCV准则来选择光滑参数h,得到f(x)的优良的非参数估计。假设{ε_4}是i.i.d.的r.v.s.,在ε_4的4阶矩有限的条件下,所选择出来的核估计及相应的Stein估计是相合的。

Suppose nonparametric regression model to be y_i=f(x_i)+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.