Bahadur Representation of Nonparametric M-Estimators for Spatial Processes  

作　　者：Jia CHEN De Gui LI Li Xin ZHANG 

机构地区：[1]Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第11期1871-1882,共12页数学学报（英文版）

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

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.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.

关 键 词：Bahadur representation local linear M-estimator spatial processes strongly mixing 

分 类 号：O212[理学—概率论与数理统计]