Local Linear Least Absolute Deviation Estimation In Semiparametric Regression Model For Contaminated Data

In biological and medical statistics,many of the observed data are sometimes affected by contaminated sources that are not part of the observed individual,and do not show true values.This kind of data is generally called contaminated data.The semiparametric regression model was put forward by Engle et al when studying the impact of climate conditions on electricity demand,in the form of Y_i=X~T_i?+g(T_i)+e_i,1?i?n.In this paper,we mainly study the parameter estimation of the new model,which is based on the mixing of the contaminated data model and the semiparametric regression model,specifi-cally,under the condition that the regression error and the contaminated source obeying Laplace distribution,which the mean value is zero and the variance is known.The least absolute devi-ation estimation method is used to estimate the linear part of the new model,the local linear estimation method is used to estimate the nonparametric part of the new model,so that the es-timation of the parameters in the original model is obtained.Then,we prove the consistency of the estimation of each parameter.In the end,the method proposed in this paper is numerically simulated,and compared with the local linear least square estimation method.According to the simulation results,it is tested that the local linear least absolute deviation estimation is effective and robust.