| This paper focuses on the robust inference in the longitudinal data analysis,including the efficient and robust generalized estimating equation(ERGEE)method and the efficient and robust empirical likelihood(EREL)method.Firstly,in Chapter 1,some basic concepts associated with the paper are introduced.Longitudinal data has a broad application in the medicine,biology,social economics and many other fields.It has drawn many researchers’ attention in recent years.The main feature of the longitudinal data is that each individual or unit is independent,but each individual or unit between the repeated measurements of the data is relevant.And because of this feature,if there are outliers in an individual measurement,there will be a series of outliers in the sample.This also makes it necessary to study the robustness of longitudinal data.Then we introduce the generalized estimating equation(GEE)method which is widely used in longitudinal data and the origin of empirical likelihood(EL)method.The most attractive is to combine the empirical likelihood inference method and the estimating equation,which is the core method to be discussed in this paper.Secondly,in Chapter 2,based on the generalized estimating equation(GEE)method of longitudinal data,a corresponding robust generalized estimating equation(RGEE)method and an effective and robust generalized estimating equation(ERGEE)method are proposed.The RGEE method mainly uses the weight function and Huber function to the Pearson residual in order to reduce the effects of outliers.While the ERGEE method introduce a new bounded exponential score function and it also reduce the impact of outliers effectively.Moreover,the asymptotic normality of the parameters estimated by the ERGEE method and the detailed algorithm are given.Thirdly,in Chapter 3,the empirical likelihood for a univariate mean is introduced in detail.Then based on the combination of the empirical likelihood method and estimating equation,a robust empirical likelihood(REL)method and an effective and robust empirical likelihood(EREL)method are proposed in the longitudinal data analysis.The large sample properties of the parameters estimated by the EREL method and the detailed algorithm are also given.The final Chapter 4 are simulation studies that includes numerical simulations and a practical study of epilepsy seizure.Numerical simulations include a continuous example of the marginal longitudinal linear model and a discrete example of the marginal longitudinal poisson model.Simulation studies have shown that robust methods play an important role in reducing the effects of outliers.The Chapter 5 is the proof of theorems,which proves the large sample properties of the parameters estimated by the ERGEE method and the EREL method. |
