纵向数据变系数单指标模型的半参数均值—协方差分析

发布时间：2018-06-08 11:53

本文选题：纵向数据 + 变系数单指标模型　；参考：《南京师范大学》2017年硕士论文

【摘要】：纵向数据广泛应用于农业、工业、生物医学、流行病学、社会经济学等领域,对其建模已成为国内外统计学者研究的热点.纵向数据的一个重要特征就是对于给定个体的重复观测间存在序列相关,如果忽略这一相关,回归函数的估计可能是无效的,因此估计协方差结构也是纵向数据分析必不可少的一部分.变系数单指标模型在参数和非参数模型间提供了一个很好地平衡,在克服非参数模型“维数灾难”问题的同时,还保留了参数模型简约性和直观解释性的优点,因此本文考虑纵向数据变系数单指标模型的半参数均值-协方差分析.本文首先阐述了纵向数据的各类统计模型及其研究现状,以及纵向数据协方差结构的研究现状.其次,引入了纵向数据变系数单指标模型,并给出了其估计的方法和步骤.具体来说,先基于方差-相关分解,对协方差结构建立了半参数的模型,分别用广义估计方程方法和伪似然方法来估计方差函数和相关结构参数;然后基于估计的协方差结构,采用轮廓迭代方法估计均值函数中的单指标参数和未知函数.最后,在一些假设条件下,建立了相关结构参数、方差函数、单指标参数和未知函数的估计的大样本性质,并分别给出了其证明.我们还通过模拟和实证分析验证了所提出估计方法的有效性.
[Abstract]:Longitudinal data are widely used in the fields of agriculture, industry, biomedicine, epidemiology, social economics and so on. An important feature of longitudinal data is that there is a sequential correlation between repeated observations for a given individual, and if this correlation is ignored, the estimation of the regression function may not be valid. Therefore, estimation covariance structure is also an essential part of longitudinal data analysis. The single index model with variable coefficient provides a good balance between parameter and nonparametric model. While overcoming the problem of "dimensionality disaster" of non-parametric model, it also retains the advantages of simplicity and intuitionistic explanation of parametric model. In this paper, we consider the semiparametric mean-covariance analysis of a single index model with variable coefficients of longitudinal data. In this paper, various statistical models of longitudinal data and their research status are described, and the research status of covariance structure of longitudinal data is also discussed in this paper. Secondly, the single index model of longitudinal data variable coefficient is introduced, and the method and steps of its estimation are given. Specifically, based on the variance-correlation decomposition, a semi-parametric model of covariance structure is established, and the generalized estimation equation method and pseudo-likelihood method are used to estimate the variance function and related structural parameters respectively, and then based on the estimated covariance structure, The method of contour iteration is used to estimate the single parameter and unknown function in the mean function. Finally, under some hypothetical conditions, the large sample properties of the estimation of correlation structure parameter, variance function, single parameter and unknown function are established, and their proofs are given respectively. We also verify the effectiveness of the proposed estimation method by simulation and empirical analysis.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C81

【参考文献】