Lack Of Longitudinal Data Semiparametric Regression Model Analysis

Longitudinal data is now a hotspot in statistics and the case of missing data occurs requently in many fields of the data research. Since the missing mechanism it is too complex to study, the regression model of the missing longitudinal data has being studied by no one. The semi-parametric regression model of missing longitudinal data is proposed in this thesis and several solutions are given:1. The longitudinal missing data is disposed by using the transformation function in this thesis. The least squares estimators of the parametric and nonparametric vectors are got, using the least squares and the kernel function method. The strong consistency and asymptotic normality ofβis proved, The weak convergence speed of g(t) is got, and the asymptotic optimality speed is Op(n1/3). In addition, through the data simulation shows that the estimate form of the method is feasible.2. For missing longitudinal data, all items will be deleted in this thesis which contains lossing data using the CC method, and only remaining "full" sample. By the second stage estination method for statistical inference, the ultimate estimates of parametric and nonparametric vector are got by using the two stages estimate. And the asymptotic normal properties of these estimators is proved. In addition, through the data simulation shows that the estimate form of the method is feasible.3. The missing longitudinal data is dealt with the fractional imputation method. Take part of the average data which is known to fill the values,using the two stages estimation method which is based on the "complete", the estimates of the parameters components and nonparametric components are gave, the ultimate estimates are got. And the asymptotic normal properties of these estimators is proved. In addition, through the data simulation shows that the estimate form of the method is feasible.Through the above aspects of the research, we initially got the feasibility estimation of the missing longitudinal data semi-parametric regression model and the estimates. A certain theoretical basis is laid for further study.