Empirical Likelihood Inference For Varying Coefficient Models With Missing Covariate Data

Varying-coefficient model has been extensively used in physiology,medicine,psychology,and social studies.The reason is that this model can deal with the "dimensional disasters" problem of nonparametric regression models on the one hand.On the other hand,it inherits the advantages of non-parametric regression model flexibility and adaptability,and it also has the advantages of parametric regression model more linear and intuitive and easy to explain.However,in practical applications,the measurement and observation of numerical values are incomplete.Therefore,in this paper,we will use empirical likelihood and composite quantile regression methods to perform statistical inference of varying-coefficient models with missing data in covariates,and give full play to the superiority of composite quantile regression method and empirical likelihood method.First of all,in the first two chapters,we introduce the research status and background knowledge related to the content of this article.The modules include missing data processing,quantile regression definition,empirical likelihood and the principle of estimating equation.Secondly,in the third chapter,we combine empirical likelihood and compound quantile regression to construct two empirical likelihood weighted estimators of ?(u)covariates with missing data and prove the asymptotic normality of the method when data are random missing.Finally,in the fourth chapter of this paper,numerical simulation,and the deviation from the standard deviation and mean-square error of different vision,using four estimation methods:no missing data estimation(Ideal),complete data estimation(CCA),inverse probability weighted estimator(IPW),the empirical likelihood weighted estimator(ELW).An estimated ?(u)comparison is made.The simulation results demonstrate that for the error distribution,data missing rate,sample size,missing mechanism and other factors.In the case of finite samples,the estimated efficiency of ELW is more effective than other methods,and the ASE of ELW is less than IPW.When the missing rate is large,the empirical likelihood method is also more effective.With the increase of the sample,the mean-square error between the IPW estimation and the ELW estimation becomes smaller,and the consistency of the two estimates can be demonstrated.