Statistical Inference Of Partially Linear Model With Measurement Error Under Censored Data

The regression problem with measurement error is a hot issue in statistics in recent years.Measurement error is a common phenomenon in biostatistics,medical science,economics and so on.If the measurement error is neglected,an attenuated estimator will be obtained,so the measurement error must be corrected by some suitable method.At the same time,partially linear model is one of semi-parametric models,which effectively combines the advantages of linear model and non-parametric model.It can fit the actual data flexibly,so it has a wide range of applications.In addition,response variables are often randomly censored in the fields of biostatistics,engineering and so on.And researches on such model are still relatively rare.There are three main types of measurement error,classical error,Berkson error,and mixed error.This paper focuses on the statistical inference of partially linear model with classical measurement error when the response variable is random right-censored data.The article first introduces two estimation methods for the parameter which are commonly used in classical measurement error model: instrumental variable method(IV)and regression calibration method(RC).The estimation results of the two methods are compared by numerical simulation.For the right-censored response variable,we construct a statistic which has the same expectation with the response variable.On this basis,instrumental variable method and regression calibration method are used to estimate the parameter part with measurement error,and the non-parametric function is fitted by local polynomial regression.Instrumental variable method needs to introduce a variable related to the explanatory variable.Then we compare linear instrumental variable method(LIV)and non-parametric instrumental variable method(NIV)with the method that neglecting the measurement error(NAE)for the parameter estimation effect through simulation,and draw fitting curve for nonparametric function.Regression calibration method assumes that the explanatory variables has normal distribution,and the main idea is using the conditional expectation to estimate the explanatory variables.The simulation results show that the true value of the explanatory variables can be effectively estimated by the regression calibration method,so that a good parameter estimation can be obtained.