The Research Of Partially Nonlinear Varying-coefficient EV Model With Missing Data

Semi-parametric regression model is a very important model in statistics,this kind of model has greater adaptability and stronger interpretation ability than simple parametric regression model and non-parametric regression model.This thesis mainly studies a partially nonlinear varying-coefficient EV model in the semi-parametric regression model,which is the generalization of partial linear variable coefficient model.The incomplete data situation is frequently encountered in practical problems,the missing data is one of the types.Research fields such as market surveys,opinion polls,environmental monitoring and reliability life tests often produce large amounts of missing data.In addition,due to the accuracy of the instrument and other problems,there will be a large number of measurement errors in the data.Data analysis for the above two types of data is often not directly utilized and requires the necessary processing of the data.Based on the above reasons,this thesis studies the statistical inference problem of partially nonlinear varying-coefficient EV model with the missing responses and measurement error.The research contents of this dissertation have the following three parts: First,for the partially nonlinear varying-coefficient EV model with missing data,we investigate the estimation of both nonparametric and parametric components by the method of inverse probability weighted local bias-corrected profile least squares,and the asymptotic normality of the estimator is proved.Second,numerical calculation is conducted under different sample size,different missing probability and different measurement error.In particular,the parameter estimation results under the condition of ignoring the measurement error and considering the measurement error are discussed when the selection probability is the same and the inverse probability weighting method is used.Simulation results shown that local bias-corrected profile least squares approach based on inverse probability weighted are workable.Third,a real data example of the heart disease assess better performance.