Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation

作     者：Li-ping Zhu Li-xing Zhu 

作者机构：East China Normal University Shanghai 200062 China Hong Kong Baptist University Hong Kong 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2006年第22卷第1期

页      面：103-114页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：华东师范大学博士基金 香港研究资助局(RGC)项目 香港浸会大学FRG项目 上海交通大学访问学者基金资助 华东师范大学博士研究生海外研修基金 

主　　题：Asymptotic normality bandwidth selection dimension reduction inverse regression method kernel estimation 

摘      要：To estimate central dimension-reduction space in multivariate nonparametric rcgression, Sliced Inverse Regression （SIR）, Sliced Average Variance Estimation （SAVE） and Slicing Average Third-moment Estimation （SAT） have been developed, Since slicing estimation has very different asymptotic behavior for SIR, and SAVE, the relevant study has been madc case by case, when the kernel estimators of SIH and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We. prove the asymptotic normality, and show that, compared with tile existing results, the kernel Slnoothing for SIR, SAVE and SAT has very similar asymptotic behavior,