Statistical Inference Of Semi-parametric Models Of Missing Data

The semi-parametric model has been widely applied in industrial,economic,biomedical and other fields since its inception in the 1980s,and its theoretical research has also been widely developed.At present,we are on the wave of the big data age,and the semi-parametric model has become a powerful tool for data analysis because of its wide applicability.However,when dealing with practical problems,due to various reasons missing data has become an unavoidable and important research problem.Under such a practical background,studying the semi-parametric model under the missing data can not only enrich its theoretical results,but also help us to promote social development and progress.In the first chapter of this paper,we introduce the research background and significance of the semi-parametric model with the missing data.Then it introduces the research status of the semi-parametric model and missing data.Finally,the structure of this paper is briefly introduced in this chapter.In the second chapter of this paper,we study the empirical likelihood(EL)estimation for the partial functional linear models with covariates missing at random.Firstly,the empirical log-likelihood ratio statistic for the unknown parametric can be constructed.Then,we proved that the proposed statistic has the asymptotic chi-square distribution.Thus,the results can be used to construct the EL confidence regions of the parameter.In the third chapter of this paper,we investigate estimation for the varying coefficient partially linear errors-in-variables model with covariates missing at random.The profile least-squares estimator for the unknown parametric is obtained by inverse probability weighted least-squares method.The asymptotic normality of the proposed estimators are proved under some appropriate conditions.Further,we construct an empirical log-likelihood ratio statistic which is shown to be asymptotic chi-square,and hence the confidence regions of the parameter component with asymptotically correct coverage probability can be constructed.A simulation study can examine the finite sample performance of the proposed methods.