基于纵向数据的秩回归和分位数回归的有效参数估计

项目名称： 基于纵向数据的秩回归和分位数回归的有效参数估计

项目编号： No.11201365

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 付利亚

作者单位： 西安交通大学

项目金额： 22万元

中文摘要： 纵向数据是指随着时间的演变追踪测得的数据。这种数据在生物研究和环境科学等领域广泛存在。在纵向数据中，由于来自同一个个体的数据间存在着潜在相关性，如何对这种相关性建模，进而提高参数估计的效是该领域研究的热点和难点问题。广义估计方程（GEE）方法是分析纵向数据常用的方法，它结合了数据的相关性，但对异常值极其敏感；基于秩回归和分位数回归的方法比较稳健，但多基于独立的模型假设构造估计方程，且估计参数及其协方差矩阵时计算量比较大。在本项目中，基于纵向数据，我们考虑稳健的秩回归和分位数回归，在数据的相关形式已知的情况下，计算反应变量的基于秩的估计函数（秩回归）和基于反应变量的示性函数（分位数回归）的协方差矩阵；利用GEE方法的想法构造估计方程；在估计参数及其协方差矩阵时，利用induced smoothing方法以降低计算量。最后，通过大量的模拟和实际数据分析评估本项目给出的参数估计的稳健性和高效性。

中文关键词： 参数估计；分位数回归；Induce smoothing方法；经验似然；纵向数据

英文摘要： Longitudinal data are collected when data are observed repeatedly over a time interval from subjects,and are very common in biological research and environmental science. There could exist underlying correlations among the data from the same subject. How to model the correlations and improve parameter estimation is hot and difficult in the analysis of longitudinal data. The generalized estimating equations (GEE) method is commonly used to analyze the longitudinal data. This method incorporates the correlations, but is very sensitive to outliers.The methods based on rank regressions and quantile regressions are robust, but most of their estimating equations are constructed based on the independence working model assumption. Moreover, the computation for estimating the parameters and their covariance matrix is very heavy. In this project, we will consider the robust rank regressions and quantile regressions with longitudinal data. Under an assumption that the correlation structure of the data is known, we will calculate the covariance matrix of the estimating functions based on the ranks of response variables (in rank regressions) and of the estimating functions based on indicator functions of response variables (in quantile regressions), and then construct estimating equations by the idea of the GEE method. We wi

英文关键词： parameter estimation；quantile regression；induced smoothing method；empirical likelihood；longitudinal data