Variable bandwidth M-estimators of the partial linear regression models

In the paper the variable bandwidth M-estimators of the partial linear models are discussed The variable bandwidth M-estimation of the unknown function and local variable bandwidth M-estimators of the unknown parameter is proposed by local linear method. Under the assumptions, the consistence and the asymptotic normality of the estimators of the unknown function and the unknown parameter are proofed. The proposed method inherits the advantages of local polynomial regression and overcomes lack of robustness of least squares techniques.