Statistical Inferences And Variable Selection For Varying Coefficient Models With Missing Responses

In this thesis,we consider the CBPS-based statistical inferences and variable selection for varying coefficient models with missing responses.We introduce the knowledge and development of varying coefficient models,missing data,empirical likelihood and variable selection in Chapter 1.The CBPS-based statistical inferences for varying coefficient models with missing response are considered in Chapter 2.Firstly,we propose the generalized method of moments estimator for propensity score based on covariate balancing.On the one hand,the statistical inferences for unknown nonparametric functions based on covariate balancing propensity score estimators and weighted imputation method are considered,the normality of the estimators of unknown nonparametric functions based on the least squares is obtained and the normal approximated confidence interval is constructed.Furthermore,we construct the empirical log-likelihood ratio statistics for nonparametric function and the proposed statistics are proved to be the chi-square distributions asymptotically,so the empirical likelihood confidence region of unknown nonparametric functions is constructed.On the other hand,we consider the interval estimation for the response mean.The normal approximated confidence interval and the empirical likelihood confidence interval are constructed.Finally,the performance of the proposed CBPS is illustrated by simulation studies and real data analysis and the results show that the CBPS-based estimators are superior to GLM-based eatimators.For Chapter 3,we develop the variable selection for varying coefficient models by the method of penalized empirical likelihood.First,the nonparametric functions are approximated by B-spline basis function,and we combine empirical likelihood loss function with SCAD penalty to select variable for models.Then,we prove the theoretical properties of variable selection under certain conditions.The Chapter 4 is the summary of this article and the future research work.