Semiparametric and Nonparametric Methods of Model Selection and Model Checking for Correlated Data

模型选择和模型检验是统计分析的基础。模型选择的主要目标是识别简洁的良好拟合模型，以平衡模型拟合的增加和模型复杂性的增加；模型检验是对所提出模型的有效性进行评估或检验。在这个研究领域有大量的文献可以作为独立的数据。然而，对于相关数据，只有零散的工作，渐近理论在很大程度上是不发达的，这主要是由于(1)缺乏丰富的一类模型，如响应的联合分布的多元高斯模型；(2)即使有这样的多元分布族，联合似然的复杂性也是如此。这些障碍使得应用为独立数据或基于全似然开发的现有模型选择和模型检查程序变得极具挑战性，如果不是不可能的话。该项目通过开发一套用于模型选择和相关数据模型检查的半参数和非参数工具来解决这一挑战，包括通过最近开发的二次推理函数和基于秩的估计方程基于矩条件的模型检查程序；数据驱动的模型检查程序，允许灵活的替代和提高一般功率性能。本课题将对大样本理论和实际性能进行深入的研究。会议还讨论了相关的研究问题，如在可能的模型错配情况下的秩回归特征，以及基于秩的模型选择算法的理论鲁棒性。相关数据经常出现在许多领域，例如生物医学和保健科学、经济学、社会科学和环境研究。这项工作将大大提高模型选择和模型检验的可用方法和理论。研究人员将开发可由统计学家和科学家轻松实现的计算包。该项目将为科学家分析高维相关数据提供新的、灵活的工具。教育将是一个重要组成部分。研究结果将纳入不同层次的统计课程。鼓励本科生和研究生，特别是来自代表性不足群体的学生参与本研究项目。

Model selection and model checking are fundamental to statistical analysis. The main objective of model selection is to identify parsimonious well-fitting models in order to balance the increase in model fit against the increase in model complexity; and that of model checking is to assess or test the validity of a proposed model. An enormous amount of literature is available for independent data in this research area. For correlated data, however, there exists only fragmented work and the asymptotic theory is largely undeveloped, mainly due to (1) the lack of a rich class of models such as multivariate Gaussian for the joint distributions of the responses, (2) the complexity of the joint likelihood even when such a multivariate family of distributions is available. These obstacles make it extremely challenging, if not impossible, to apply existing model selection and model checking procedures that were developed for independent data or based on full likelihood. This project addresses this challenge by developing a set of semiparametric and nonparametric tools for model selection and model checking for correlated data, including model checking procedures based on moment conditions via the recently developed quadratic inference function and rank-based estimation equations; data-driven model checking procedures that allow for flexible alternative and increase general power performance. The large sample theory and practical performance will be investigated in depth in this project. Also on the agenda are related research issues, such as the characterization of rank regression under possible model misspecification and the theoretical robustness properties of rank-based model selection algorithms.Correlated data frequently occur in many fields, such as biomedical and health sciences, economics, social sciences and environmental studies. This work will greatly enhance the available methodologies and theories for model selection and model checking. The investigator will develop computational packages that can be easily implemented by statisticians and scientists. This project will provide scientists with new and flexible tools for analyzing high-dimensional correlated data. Education will be an important component. The research results will be incorporated at different levels of statistical courses. Undergraduate and graduate students, especially those from underrepresented groups, will be encouraged to participate in this research project.