Double Robustness Of Inverse Probability Weighted Estimators With Missing Data

As early as the 1870's,statistical analysis of missing data has ever been pros-perous. Missing data is an ubiquitous problem in medical and social science stud-ies,which is the very important research subject.Semiparametric regression models overall the merit of parametric regression models and nonparametric regression models.In actual life, semiparametric regression models are more flexible than parametric regression models and nonparametric regression models and therefor more explanatory and useful.The oldest inverse probability weighting method is the method of Horvitz and Thompson [5] in 1952,which re-weights each observed yi. For any individual randomly chosen from a population with covariate value X,the probability that such an individual will have complete data isπ(X).Therefore, any individual with covariate X with complete data can be thought of as representing1/π(X) individuals at random from the population,some of which may have missing data.The aim of the thesis is to study the doubly robustness of inverse probabil-ity weighted estimators of the mean value in the parametric and partially linear models.By using imputation method of missing data promoted by Qin Jing [8]etc,we construct inverse probability weighted estimator of mean value with the responses missing at random.The basic idea is as follows.By the MAR assumption,we firstly find the imputation of missing responses in the parametric models,then we gain the estimators of mean valueμIPW by inverse probability weighing methods.We prove doubly robustness and asymptotic distribution ofμIPW.We compare the efficiency betweenμER andμIPW. On that basis,we apply our estimator methods to partially linear models.At last,our simulation results show the merits of inverse probability weighing estimators.