An Investigation into Small Sample Properties of Estimators for Marginal Models (Mathematics)

本研究的目的是提供有关最近提出的几种估计边际模型平均参数的方法的小样本特性的信息。重点将放在广义估计方程方法（Liang和Zeger, 1986； Zhao和Prentice, 1990； Prentice和Zhao， 1991）和在这种情况下估计的似然方法（Fitzmaurice和Laird， 1993）。这些模型适用于收集相关观察的群集样本，如在纵向研究中。当相关响应测度是离散的或不能用多元正态分布来建模，并且同时存在时变和时平稳的连续协变量时，就迫切需要这种方法。缺失数据对小样本性质的影响也将被评估。大规模计算机模拟将用于解决这些问题，并注意计算问题和所需资源。互动活动包括：为统计学学生讲授研究生课程；参加关于纵向数据的研究生课程；组织与本研究相关主题的一系列小型课程；研讨会;非正式组织;和学生一起参观当地的统计机构。

The objective of this research is to provide information regarding the small sample properties of several recently proposed methodologies for estimating marginal model mean parameters. Focus will be on the generalized estimating equation methodology (Liang and Zeger, 1986, Zhao and Prentice, 1990, Prentice and Zhao, 1991) and a likelihood approach to estimation in this setting (Fitzmaurice and Laird, 1993). These models are applicable when a sample of clusters of correlated observations is collected, as in a longitudinal study. The critical need for such methods is when the correlated response measures are discrete or cannot be modelled with a multivariate normal distribution, and there are both time- varying and time-stationary continuous covariates. The impact of missing data on the small sample properties will also be assessed. Large-scale computer simulations will be used to address these questions, with attention paid to computational concerns and required resources. The interactive activities include: teaching a graduate-level course to statistics students; participating in a graduate-level course on longitudinal data; organizing a series of mini-courses on topics related to this research; seminars; informal groups; and visiting local area statistical organizations with students.