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Consistency and Normality of M-Estimators in Partly Linear Models with Stochastic Adapted Errors |
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| Authors: | Li Yan Xia Chen |
| Institution: | 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. |
| Keywords: | Piecewise polynomial Partly linear model M-estimator Stochastic adapted sequence |