Statistical Inference On Varying-coefficient Partially Linear Models With Multiplicative Distortion Measurement Errors

The varying-coefficient partially linear model is not only flexible and easy to explain the problems,but also can avoid ”dimensional disaster”,enhance the fitting effect of the model,in biology,informatics,finance,economics,humanities and other fields have been widely used.However,in the processing of practical problems,for some reason,the varying-coefficient partially linear model may be established with measurement errors.At this time,the original traditional estimation method cannot be used,so a new and effective estimation method needs to be adopted.This paper focuses on the estimation and variable selection of varying coefficient partially linear models with multiplicative distortion measurement errors.For varying coefficient partially linear models,which the response variable and covariates in the linear part are measured with multiplicative distortion measurement errors,we construct the estimators for unknown parameters and varying coefficient functions in the model using the covariate calibration and Profile least squares estimation procedures.Large sample properties of the proposed estimators are established under the right conditions.Moreover,a large number of numerical simulations are presented to illustrate that the proposed estimation procedure are effective.For the variable selection problem under the same model,which response variable and covariates in the linear part are measured with multiplicative distortion measurement errors.We derive the estimators for unknown parameters and varying coefficient functions based on SCAD-penalized least squares estimation.We also proved the asymptotic properties for the proposed estimators under some assumptions.Similarly,extensive numerical simulations are conducted to further examine the effectiveness of the proposed procedure.