Regression Analysis of Networked Data: Estimating Function Theory and Applications

网络数据在实践中是普遍存在的，如遗传网络数据和社会网络数据。需要对网络数据进行回归分析，以了解一组网络相关结果与另一组协变量之间的关系。完成这一任务需要快速有效的模型参数估计和推断方法。这促使研究人员开发一种新的回归建模框架，用于无向边网络或有向边网络中的数据。通过PI在流行病学，环境健康科学和肾脏病学方面的长期合作，当地科学家可以使用所研究的方法，并提供有价值的反馈。这个新的研究项目也可以导致大量的教育举措，将涉及本科生和研究生，并使他们接触到与相应研究相关的各种跨学科主题的最先进的研究。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。这些和其他传播活动将提高认识的现代强大的数据分析方法之间的科学家从其他field.Although网络分析已被广泛研究的文献中的依赖结构，很少有人研究还在回归分析的响应协变量关系。这个项目试图通过几个步骤来填补这一空白。具体来说，PI建议研究三个不同但相关的问题，包括网络依赖模型，通过广义矩方法估计函数方法和大样本理论。这个研究项目包括几个创新和有效的统计程序的基础上估计和推断的估计函数。预计所研究的框架将允许研究人员处理各种网络相关的离散和连续数据。

Network data are pervasive in practice such as genetic network data and social network data. Regression analysis of network data is needed to understand the relationship between a set of network-correlated outcomes and another set of covariates. Accomplishing this task requires fast and efficient estimation and inference methods for the model parameters. This motivates researchers to develop a new regression modeling framework for data arising from either networks with undirected edges or networks with directed edges. Through PI's long-term collaborations in Epidemiology, Environmental Health Sciences, and Nephrology, the studied methods can be used by local scientists who will provide valuable feedback. This new research project can also lead to substantial educational initiatives that will involve undergraduate and graduate students and expose them to the state-of-the-art research in various interdisciplinary topics related to the corresponding 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.Although the network analysis has been extensively studied in the literature for dependent structures, little has been studied yet in the regression analysis of response-covariate relationships. This project attempts to fill in such a gap through a few steps. Specifically, the PI proposes to study three different but related problems, including network dependence models, estimating functions methodology via the generalized method of moments, and large-sample theory. This research project includes several innovative and efficient statistical procedures based on estimating functions for estimation and inference. It is anticipated that the studied framework will allow researchers to handle a large variety of network-correlated discrete and continuous data.