纵向数据的动态半参数建模及其统计推断

项目名称： 纵向数据的动态半参数建模及其统计推断

项目编号： No.11471203

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 尤进红

作者单位： 上海财经大学

项目金额： 57万元

中文摘要： 纵向数据动态半参数模型是一种崭新的纵向数据建模方法。它允许在每个观测时间点每个解释变量对响应的影响是非线性、未知的，同时允许这种影响随着观测时间的变化而变化。由此极大地增加了建模的灵活性。在更大程度上避免了建模的系统偏差。通常的纵向数据可加模型、变系数模型以及单指标模型都是它的特例。对纵向数据动态半参数模型的研究在国际和国内还处于起始阶段。本项目旨在系统地研究纵向数据的动态半参数建模及其相应的统计推断。我们将创造性地结合紧积B样条，局部多项式以及估计方程等技巧，提出纵向数据动态半参数模型中未知曲线、曲面以及参数的有效估计，建立它们的大样本性质。并以此为基础提出辨别纵向数据可加模型和纵向数据变系数模型以及模型动态性的有效方法。除此之外，我们还将涉及纵向数据动态分位数模型的统计推断。最后，我们将提出的方法用于分析实际数据，为实务部门决策提供更加可靠的依据。此项目具有重要的理论意义与应用价值。

中文关键词： 生物统计；纵向数据；统计推断；半参数模型；动态建模

英文摘要： The longitudinal data dynamic semiparametric model is a new semiparametric longitudinal data modeling method. At each time pont, it allows the relationship between the explanatory variables and response variable is nonlinear and unknown . In the meantime, it allows this relationship to change with the time. Therefore, it increases the flexiblity of modeling and reduces the modeling bias greatly. The usual longitudinal data additive model, longitudinal data varying coefficient model and longitudinal data single index model are its sepcial case. In the world wide, the research about the statistical inference of the longitduinal data dynamic semiparametric model is still at the beginning. The aim of this project is to make a systematic resarch for the statistical inference of the longitudinal data dynamic semiparametric model. We will combine the tensor product B spline series approximation, local polynomial smoothing and generalized estimation equation techniques and propose the efficeint estimators for the unknown curves, unknown surfaces and unknown parameters. In addition, we will establish the large sample properties of these resultant estimators. Beasd on these results, we will develop new methods to make modeling tests for the usual longitudinal data additive model and longitudinal data varying coefficient model，and check the model dynamics. We will also invlove the statistical inference of the semiparametric longitudinal data dynamic quantile model. Finally, we will apply the proposed methods to the real data analysis and provide the resports to the companies and govements. This project is very important in the theoretical sense and also applicable.

英文关键词： Biostatistics;Longitudinal Data;Statistical Inference;Semiparametric Model;Dynamic Modeling