Bahadur Representation of Nonparametric M-Estimators for Spatial Processes

作     者：Jia CHEN De Gui LI Li Xin ZHANG 

作者机构：Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2008年第24卷第11期

页      面：1871-1882页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China (No.10771192) 

主　　题：Bahadur representation local linear M-estimator spatial processes strongly mixing 

摘      要：Under some mild conditions, we establish a strong Bahadur representation of a general class of nonparametric local linear M-estimators for mixing processes on a random field. If the socalled optimal bandwidth hn = O（｜n｜^-1/5）, n ∈ Z^d, is chosen, then the remainder rates in the Bahadur representation for the local M-estimators of the regression function and its derivative are of order O（｜n｜^-4/5 log ｜n｜）. Moreover, we derive some asymptotic properties for the nonparametric local linear M-estimators as applications of our result.