基于广义Hille引理及扰动想法之下的一种非参数回归方法

Nonparametric regression using generalized Hille's Lemma and perturbation

近几十年来,非参数回归的研究方兴未艾.针对Fan(1992,1993,2003)局部核函数法的2个缺陷,该文基于广Hille引理及扰动思想提出了一种新的回归方法,新的回归估计量具有逐点一致性及最优渐进均方误差.该文还利用CV技术及ISE标准对该回归估计的光滑参数进行最优筛选,模拟结果表明:与Fan(1992,1993,2003)中的方法相比,在大样本下该文所提出回归方法有更佳估计效果.

Based on a generalization of Hille’s lemma and an idea of a perturbation,this paper proposes a new regression estimation.The theoretical Point-wise consistency and asymptotic MSE（Mean Squared Error） are derived.The CV（cross-validation） selection technique and ISE（Integrated Squared Error） criteria are applied for the optimal value of smoothing parameter.The simulation results show that the new estimator in large sample has superiority,comparing with Fan（1992,1993, 2003）’s established local kernel estimation.