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.
基金
National Natural Science Foundation of China (No.10771192)