Statistical Inference In Semiparametric Varying-coefficient Partially Linear Models With Missing Data

In this thesis, we mainly consider the estimation of semiparametric varying-coefficient par-tially linear model with missing data. The thesis is divided into two parts. In the first part, forthe semiparametric varying-coefficient partially linear model with covariate missing at random,we investigate the estimation of both parametric and nonparametric components. In order todeal with missing data, logistic parametric models are applied to estimate missing probability,which not only avoiding the curse of dimensionality, but also easy to calculate. In this paper,we obtained the estimators of parametric and nonparametric components by inverse probabilityweighted least-squares method. The resulting estimators are shown to be asymptotic normal-ity. A simulation study is conducted to illustrate the finite sample performance of the proposedmethod. In the second part, we constructed the confidence regions of parametric components forthe semiparametric varying-coefficient partially linear model based on the empirial-likelihoodmethod. Combining with the inverse probability weighted approach, an empirical log-likelihoodstatistic is proposed. It is shown that the proposed statistic is asymtotically chi-squared distribu-tion. Thus, it can be used to construct the confidence regions of parametric components. Sim-ulation results and a real data analysis shown that the empirical-likelihood inference approachbased on the inverse probability weighted are assess better finite sample performance.There are two distinguished features in this thesis: Firstly, the semiparametric varying-coefficient partially linear model is considered in many literatures currently under independentdata, longitudinal data and response variable missing at random and so on, but this paper stud-ies the statistical inference of this model with covariate missing at random. Secondly, we notonly consider the estimators and their asymptotic normality of the parametric and nonparametriccomponents based on the inverse probability weighted least-squares method, but also structureempirical log-likelihood ratio function and study the confidence region of parametric compo-nents by the inverse probability weighted approach.