Regression Analysis of Networked Data: Estimating Function Theory and Applications

网络数据在实践中无处不在，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，以了解一组与网络相关的结果与另一组协变量之间的关系。要完成这一任务，需要对模型参数进行快速有效的估计和推断。这促使研究人员开发一种新的回归建模框架，用于从具有无向边的网络或具有有向边的网络产生的数据。通过PI在流行病学、环境健康科学和肾脏病方面的长期合作，所研究的方法可以被当地科学家使用，他们将提供宝贵的反馈。这一新的研究项目还可以带来大量的教育举措，让本科生和研究生参与进来，让他们接触到与相应研究相关的各种跨学科主题的最新研究。这些课程包括新课程、大型会议的短期课程、暑期研讨会、指导和软件开发。这些和其他传播活动将提高来自其他领域的科学家对现代强大的数据分析方法的认识。尽管网络分析在文献中已被广泛研究相依结构，但在响应-协变量关系的回归分析中还鲜有研究。这个项目试图通过几个步骤来填补这一空白。具体地说，PI建议研究三个不同但相关的问题，包括网络依赖模型、基于广义矩方法的函数估计方法和大样本理论。这项研究项目包括几个创新和有效的统计程序，基于估计函数进行估计和推理。预计所研究的框架将允许研究人员处理大量与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.