Consistency Of Estimators In The Partially Linear Varying-coefficient EV Models Under Restricted Condition

Partially linear varying-coefficient model is a model with strong practical application proposed in recent years.The model contains a number of sub-models,such as parameters,on parametric and semi-parametric models.n.Therefore,it not only combines the advantages of linear model,which is easy to explain with robust features of non-parametric model but also dynamically makes the expression of corresponding relationship between covariates and corresponding variables.In the classical regression model,it is usually assumed that the observed data are complete and accurate.And the error terms are independent of each other.But in reality,the mastered data basically have measurement errors,or even lacks response variables.In addition,there is usually limited or assumed conditions in the actual state,making the model parameters tend to have a certain binding.In this paper,it is assumed that these constraints are used to estimate the coefficients and coefficient functions of the model and discuss their properties.In the first chapter of this paper,the research background,current situation and common theory of partial linear EV model are mainly introduced.This paper introduces the background of the simulation research and the required knowledge.In the second chapter,research on the partial linear EV model with non-parametric part with measurement error under linear constraint condition is made.Estimation of unknown parameters and coefficient functions in the model is conducted by adjusted weighted least squares.The consistency of nonparametric and parametric functions is proved and the model test results are obtained.In the third chapter,the research on partial linear variable coefficient(EV)model with the measurement error in the parameter part and the nonparametric part is conducted when the linear constraint condition and the corresponding variable are missing.The unknown parameters and the coefficients function are estimated by using the least squares method of profile,local correction and Lagrange multiplier.