Inference and computational methods for regression models in the presence of partially observed network data or high-dimensional capture-recapture data

该发现研究计划关注响应驱动采样（RDS）和捕获-再捕获实验的统计模型的开发，以应对数据分析中的新理论和方法挑战。它把重点放在基础理论和计算方面的新的统计模型在部分观察到的网络数据或高维捕获-再捕获数据的存在。 对于RDS，我们将首先解决回归模型的参数估计问题，在一个新的参数识别范式下，当底层的人口网络是部分观察。我们将提出新的半参数估计方法下温和的拓扑约束的网络结构和额外的模型假设。然后，我们将放松拓扑约束，并提出部分识别下的目标参数的识别区域。一旦这些原则性的RDS回归方法的开发，在RDS研究的因果推理框架将被提出。此外，将通过对RDS过程建模来开发两个新的基于设计和基于模型的人口规模估计器：（i）作为波浪式抽样设计，并对招募数据的所有可能的重新排序进行平均，以及（ii）作为捕获-再捕获“删除”模型，其中个人的招募概率取决于其网络大小或程度。 在capture-recapture中，将详细阐述新的模型和计算方法，以分析通过激活移动的手机上的应用程序生成的具有底层网络结构的高维营销数据，重点是在因果框架下估计数字广告对客流量的直接和间接影响。我们将采用潜在结果框架，并假设个人对广告的暴露可能会影响她/他的邻居访问公共场所的决定。该研究计划的计算方面将进一步开发和实施开放获取软件，以供研究人员和用户更广泛地使用。该发现研究计划将为通过捕获-再捕获和RDS收集的数据的现代分析提供理论和方法学基础。这将为这些数据收集和分析设计提供新的理解，这将有助于公共卫生，社会科学以及营销和计算广告等新领域的应用。

This Discovery research program is concerned with the development of statistical models for respondent-driven sampling (RDS) and capture-recapture experiments to tackle new theoretical and methodological challenges in data analysis. It puts the emphasis on the underlying theory and the computational aspects of new statistical models in the presence of partially observed network data or high-dimensional capture-recapture data. For RDS, we will first tackle the parameter estimation problem of regression models, under a new parameter identification paradigm, when the underlying population network is partially observed. We will propose novel semiparametric estimation methods under mild topological constraints on the structure of the network and under additional model assumptions. We will then relax the topological constraints and propose identification regions for the target parameters under partial identification. Once these principled approaches for RDS regression are developed, a framework for causal inference in RDS studies will be proposed. Further, two new design-based and model-based population size estimators will be developed by modeling the RDS process (i) as a wave-wise sampling design and by averaging over all possible reordering of the recruitment data and (ii) as a capture-recapture `removal' model in which individuals' recruitment probabilities depend on their network sizes, or degrees. In capture-recapture, new models and computational methods will be elaborated to analyze high-dimensional marketing data with an underlying network structure, generated by activating applications on mobile phones, with a focus on the estimation of direct and indirect effects of digital ads on foot traffic under a causal framework. We will adopt the potential outcome framework, with the additional assumption that an individual's exposition to an ad may affect her/his neighbors' decision to visit public places. The computational aspect of this research program will be further developed and implemented in open access software for a wider uptake by researchers and users. This Discovery research program will provide theoretical and methodological foundations for modern analysis of data collected via capture-recapture and RDS. This will offer a new understanding of these designs for data collection and analysis, which will be useful for applications in public health, social sciences, and new areas such as marketing and computational advertising.