Composite Estimating Function Approaches to GeoCopula Models for Complex Spatially Correlated Data

技术的最新进展为主题科学家提供了强大的工具来进行大规模实验和收集复杂的空间相关数据。该提案的重点是发展用于分析这种高维复杂数据的统计模型和复合似然方法。具体而言，研究者计划实现三个研究目标：为时空数据、空间聚类数据和空间网络数据建立一个具有灵活和理想相关结构的多变量copula模型的统一框架;在所提出的模型中建立一个可行的和计算上易于处理的估计和推理方法以及算法;建立了复合估计函数（JCEF）估计量的大样本理论。 所有提出的统计模型和方法将被应用于分析实际研究的数据，以促进对主题科学的理解，并最终提高人类的知识和生活质量。该研究员与密歇根大学的流行病学、环境健康科学、传染病和交通安全政策等其他领域的研究人员有着密切的联系。他一直与这些科学家密切合作，他们将成为这些方法的当地用户，并提供宝贵的反馈。该项目还致力于实质性的教育举措，将涉及本科生和研究生，并使他们接触到与拟议研究有关的各种跨学科主题的最新研究。其中包括新课程、主要会议的短期课程、夏季讲习班、指导和软件开发。这些活动和其他传播活动将提高其他领域科学家对现代强大数据分析方法的认识。

Recent advances in technologies have given subject-matter scientists powerful tools to conduct large scale experiments and collect complex spatially correlated data. This proposal focuses on the development of statistical models and methods of composite likelihood for analyzing such high-dimensional complex data. In particular, the investigator plans to achieve three research goals: To develop a unified framework of multivariate copula models with flexible and desirable correlation structures for spatio-temporal data, spatial-clustered data and spatial-network data; to develop a feasible and computationally tractable estimation and inference methods as well as algorithms in the proposed models; and to establish the large-sample theory for the proposed composite estimating function (JCEF) estimator. All the proposed statistical models and methods will be applied to analyze data from practical studies to facilitate the understanding of subject-matter sciences and ultimately to improve human knowledge and quality of life. The investigator has close connections with researchers in other fields such as Epidemiology, Environmental Health Sciences, Infectious Diseases and Policy in Transportation Safety at University of Michigan. He has been working closely with these scientists who will serve as local users of the methodologies and provide valuable feedback. The project is also devoted to substantial educational initiatives that will involve undergraduate and graduate students and expose them to state-of-the-art research in various interdisciplinary topics related to the proposed research. These include new courses, short courses at major conferences, summer workshops, mentoring, and software development. These and other dissemination activities will increase awareness of modern powerful methods for data analysis among scientists from other fields.