The Research Of Two Kinds Of Models With Missing Data

In statistical analysis,the phenomenon of missing data is very common.For example,in the fields of clinical experiments,social investigations,industrial trials,etc.Because some uncontrollable willingness such as the respondents refused to answer or incomplete recording of experimental results,we cannot obtain all the observation data.Therefore,classic statistical methods and theories cannot be applied to the corresponding statistical inference.A large number of scholars have proposed many methods for dealing with missing data.We first use the idea of inverse probability weighting to consider the parameter and non-parameter estimation of the additive partially nonlinear model with missing covariates,and then use the idea of the augmented inverse probability weighting to study the model average of the linear model with missing responses.Specifically,the research contents of this paper are composed of the following aspects:In Chapter 1,We first introduced the research background and current status of this article,and finally listed the main work and structure of this article.Firstly,the least squares estimation and empirical likelihood inference of the additive partially nonlinear model with missing covariates is considered in Chapter2.In this chapter,we first present the quasi-likelihood estimation method to obtain estimation of the propensity score.Then we use the idea of inverse probability weighting to give least squares estimation of the paramertric components and prove the asymptotic normality of the estimation.Then,using inverse probability weighting method,the empirical log-likelihood ratio statistics for the parametric and nonparametric components are proposed.Under certain conditions,the proposed statistics are proved to be the chi-square distributions asymptotically.The confidence regions for the parameter and the point-wise confidence intervals for coefficient function are constructed.At last,simulation studies are conducted to examine the performance of the proposed methods.For the parameter part,we compare the empirical likelihood method with the normal approximation method,and the results show that the empirical likelihood method is better than the normal approximation.For the nonparametric part,the Quantile-Quantile plots further verify the theoretical result.In Chapter 3,we mainly study the model selection and frequency model averaging methods of linear regression models with missing responses.First,the covariate balanced propensity score(CBPS)method is used to estimate the unknown parameters in the propensity score function.Then we give the estimation of the regression coefficients of each sub-model by the augmented inverse probability weighting method and prove the asymptotic normality of these estimators.Finally,the FIC criterion is given based on the approximate unbiased estimation for the asymptotic variance of the target parameter.We discusse the asymptotic property of the average estimation of the frequency model,and construct the confidence interval for the target parameter.In Chapter 4,we summarize the main contents of this thesis and give the contents for future research.