一类相关结构下纵向数据的两步估计法  

Two-step Estimation for Longitudinal Data When the Inverse of the Working Correlation Matrix is a Linear Combination of Some Known Matrices

作　　者：李玉玲[1] 高巍 LI Yu-ling;GAO Wei(School of Applied Mathematics,Beijing Normal University,Zhuhai 519085,China;School of Mathematics and Statistics,Northeast Normal University,Changchun 130021,China)

机构地区：[1]北京师范大学珠海分校应用数学学院,广东珠海519085 [2]东北师范大学数学与统计学院,吉林长春130021

出　　处：《数学的实践与认识》2021年第13期157-165,共9页Mathematics in Practice and Theory

基　　金：广东省普通高校特色创新项目(201912009QX)。

摘　　要：主要研究当相关矩阵的逆矩阵可以表示为一些已知矩阵的线性组合时,纵向数据的参数估计问题.纵向数据分析中最常用的模型是广义线性模型.而广义线性模型的最根本问题是如何利用数据的组间相关性来提高统计推断的准确度和效率.目前应用最广泛的方法是广义估计方程方法.尽管当工具相关矩阵被错误建模时,该方法仍能保证估计的相合性,但估计的效率会大大降低.为避免工作相关矩阵的错误建模,提出了一种新的估计法,可以有效地处理纵向数据的组内相关性.证明了该估计法的渐进正态性质,并通过模拟计算和实例分析说明了该估计法的稳健性.In this paper,we mainly interested in the statistics inference on parameters when the inverse of the correlation matrix is a linear combination of some known matrices.The generalized estimating equation approach proposed by Liang and Zeger is perhaps one of the most widely used methods for longitudinal data analysis.While this method guarantees the consistency of its estimators under working correlation structure misspecification,the corresponding efficiency can be severely affected.In this paper,we propose a two-step estimation method.Asymptotic properties of the two-step estimators are developed.We illustrate the methodology with data analysis and simulation studies.Finally,we provides a concluding discussion.

关 键 词：广义估计方程 纵向数据 二元推断函数 两步估计法 

分 类 号：O212.1[理学—概率论与数理统计]