Consistency and Normality of M-Estimators in Partly Linear Models with Stochastic Adapted Errors

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.