Estimation Of Two Kinds Of Semiparametric Models With Additive Distortion Measurement Errors

The semiparametric regression model can not only avoids the “curse of dimensionality”,but also fully excavate the information between the data and enhance the fitting effect of the model.It is widely used in the fields of economics,finance,biomedicine and sociology.However,in some practical problems,due to various reasons,the semiparametric model may be established with measurement errors.At this time,traditional estimation methods are no longer applicable,and new and effective estimation methods need to be developed.This paper focuses on the estimation of varying coefficient partially linear models and partially linear additive models with additive distortion measurement errors.For varying coefficient partially linear models,when the response variable and covariates in the linear part are measured with additive distortion measurement errors,we proposed the estimators for unknown parameters and varying coefficient functions in the model based on the covariate calibration and Profile least squares estimation procedures.Asymptotic properties of the proposed estimators are established under certain conditions.In addition,a large number of numerical simulations are presented to illustrate the proposed estimation procedure are effective.For partially linear additive models,when response variable and covariates in the linear part are measured with additive distortion measurement errors,we derive the estimators for unknown parameters and additive nonparametric functions based on the model transformation and B-splines function approximation.We also proved the large sample nature for the proposed estimators under weak assumptions.Similarly,extensive numerical simulations are conducted to further examine the effectiveness of the proposed procedure.