1. College of Mathematics and Information Science , Shaanxi Normal University , Xi'an , China lyan@snnu.edu.cn;3. College of Mathematics and Information Science , Shaanxi Normal University , Xi'an , China
Abstract:
The robust M-estimators for the partly linear model under stochastic adapted errors are considered. It is shown that the M-estimator of parameter is asymptotically normal and the M-estimator of the nonparametric function achieves the optimal rate of convergence for nonparametric regression. Some known results are improved and generalized. Some simulations and a real data example are conducted to illustrate the proposed method.