Coefficient Functions Estimation And Property In Varying-Coefficient Errors-in-Variables Models With Missing Response Variables

Varying coefficient model is proposed by Hastie and Tibshhirani in1993, be-cause it can avoid the "dimensionality curse" problem, has the parametric and non-parametric regression model’s easily to explain, flexible and robust features, etc. has attracted the attention of many statisticians.However, in practical problems, due to inaccurate measurement tools, some people do not cooperate with the in-vestigation and other reasons, it is difficult to obtain accurate measurements and all measured values of some variables, therefore it is a common phenomenon that encountered complex data,such as measurement error data,missing data, verifying data, pollution data and so on. How to make an inference in the case of these com-plex statistical data exist, has become one of the hot issues in the field of statistics.This paper will examine varying coefficient model and Adaptive varying coeffi-cient model which is a generalized form of varying coefficient model in the missing data and the measurement error data.Firstly, consider the coefficient functionsβ(U)estimation of the varying coeffi-cient model with measurement error in covariant variables and the response vari-able with missing data. The estimation of coefficient functions are considered in complete observation data and the interpolation data, and the asymptotic normal-ity of estimation is proved. Then verify the excellent properties of the estimation method by numerical simulation. Secondly, discuss the coefficient functionsgj(·)(j=0,1,…, n)two step estimation of Adaptive Varying-Coefficient Errors-in-variables Models with missing response variable by using kernel estimation method,prove asymptotic properties of the estimation value and consistency properties, the two step estimation values are compared by the numerical simulation, and the second step estimation is better than the first step.