Stahel-Donoho kernel estimation for fixed design nonparametric regression models  

作　　者：LIN Lu CUI Xia 

机构地区：[1]School of Mathematics and System Sciences,Shandong University,Ji'nan 250100,China School of Mathematics and System Sciences,Shandong University,Ji'nan 250100,China

出　　处：《Science China Mathematics》2006年第12期1879-1896,共18页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No.10371059).

摘　　要：This paper reports a robust kernel estimation for fixed design nonparametric regression models.A Stahel-Donoho kernel estimation is introduced,in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points.Based on a local approximation,a computational technique is given to approximate to the incomputable depths of the errors.As a result the new estimator is computationally efficient.The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error.Unlike the depth-weighted estimator for parametric regression models,this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one.Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.This paper reports a robust kernel estimation for fixed design nonparametric regression models. A Stahel-Donoho kernel estimation is introduced, in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points. Based on a local approximation, a computational technique is given to approximate to the incomputable depths of the errors. As a result the new estimator is computationally efficient. The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error. Unlike the depth-weighted estimator for parametric regression models, this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one. Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.

关 键 词：NONPARAMETRIC regression kernel estimation statistical depth robustness. 

分 类 号：N[自然科学总论]