Estimation Methods And Theories Of Several Classes Of Regression Models With Missing Data

Missing data and measurement error data are frequently encountered in prac-tical problems.The existing statistical theories and methods of dealing with full data are no longer applicable.So it is necessary to seek new methods to make statistical analysis for these data.Inverse probability weighting method and im-putation method are two main methods for dealing with missing data.However,researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimators.Therefore,in this dissertation,we mainly study the estimation of interest parameters for linear regression model,nonlinear regression model and partially linear model with missing data and mea-surement error data.More specifically,the research contents of this dissertation have the following five parts:For the linear regression model with response missing at random,firstly,based on covariate balancing propensity score and generalized method of moments,the estimators of coefficients in propensity score model are obtained.Secondly,by means of the estimators,we construct estimators of the regression parameters and the mean of response by making use of least square method and empirical likeli-hood with imputed values,and we study their asymptotic properties under some regularity conditions.The estimators based on covariate balancing propensity score are compared with those based on generalized linear method.For the nonlinear regression model with missing response,firstly,based on em-pirical likelihood method,we obtain the estimators of propensity score model.Sec-ondly,based on inverse probability weighted imputation and least square method,the estimators of the regression parameters and the mean of response are con-structed,their asymptotic properties are studied.Simulation studies show that the proposed method is workable.For the partially linear model with response missing at random,firstly,based on covariate balancing condition and empirical likelihood method,the estimators of propensity score model are derived.Secondly,based on the estimators and inverse probability weighted imputation method,the estimators of the regression parameters and the mean of response are constructed,and their asymptotic prop-erties are established.Some simulation studies are undertaken to assess the finite sample performance of the proposed methods.For the linear regression model with covariate missing at random,we mainly consider the estimation of regression coefficient.Firstly,we propose response bal-ancing propensity score method,and obtain the estimators of propensity score model by taking advantage of empirical likelihood method.We prove the asymp-totic properties of the estimator.Secondly,the inverse probability weighting esti-mators of the regression coefficient are constructed based on least square method and empirical likelihood method and the asymptotic properties of the estimators are derived.Simulation study shows that the proposed methods perform well.For the partially linear models with missing responses and measurement error in the nonparametric part,we focus on the estimation of response mean.Firstly,based on the deconvolution method,the estimator of the nonparametric compo-nent with errors in variables is obtained,the estimator of parametric component is derived accordingly.Secondly,by advantage of the inverse marginal probabil-ity weighted method,we construct the estimator of response mean and study the asymptotic normality of the proposed estimator.Finally,simulation study shows that the proposed method is workable.