The Response Variable Random Missing Part Of The Linear Model Of Statistical Inference

The partially linear model is an important semiparametric statistical model, and it is widely used in various fields. Many methods and techniques have been proposed and studied. But in actual application, we can not obtain accurate data easily. On the contrary, we usually get some data with errors. Meanwhile missing data are unavoidable because of the differences of the data obtaining methods and the understanding of data structure. These are the reasons why the research of missing data is so popular. In semiparametric regression models, penalized splines can be used to describe complex, non-linear relationships between the mean response and covariates. So we describe a method for estimating the partially linear model on penalized splines within a linear mixed model framework.In this thesis, we considered the partially linear model when the responses are missing at random. There are mainly five parts. In the first chapter, we introduce the general development of the partially linear model, missing data and summarize the methods. In the second chapter, we introduce Imputation, semiparametric regression surrogate and inverse marginal probability weighted approaches to estimate the regression coefficients and the nonparametric function, respectively. All the proposed estimators for the regression coefficients are shown to be asymptotically normal, and the estimators for the nonparametric function are proved to converge at an optimal rate. In the third chapter, we develop Imputation, semiparametric regression surrogate method for estimating the model on penalized splines within a linear mixed model framework. Then a simulation study is conducted to compare the finite sample behavior of the proposed estimators in chapter four. We briefly review the main contents of this thesis, and propose some suggestions to the future work in the last chapter.