A Spectral Framework for Network-Driven Sampling

概率抽样极大地减轻了各个学科的研究负担，因为统计推断可以将样本的结论扩展到整个人群。然而，经典的抽样技术需要一个抽样框架，列出群体中的每个个体和联系每个个体的方式。在许多情况下，采样帧是不可用的。在其他情况下，采样帧的编制成本太高，或者只覆盖了总体的一个有偏差的子集。特别是对于难以接触到的人群，网络驱动的抽样是找到人群成员的唯一方法之一。利用网络来寻找目标人群出现在许多学科中，有许多名称：受访者驱动抽样、雪球抽样、网络爬行、链接跟踪、广度优先搜索、共同免疫沉淀和染色质免疫沉淀。这些不同的技术都通过要求参与者推荐朋友来提供难以接触到的网络人群。因此，这些都是网络驱动的技术。经典的抽样理论不适用于网络驱动的抽样，因为朋友是相似的；这就导致了受潜在社会网络影响的样本之间的依赖关系。调查人员进行的初步研究确定了一个关键阈值，该阈值将社会网络的结构与抽样树中的推荐率联系起来；超过这个临界阈值，标准的网络驱动方法产生高度不确定的估计。这项研究的目的是产生新的统计技术，继续执行远远超过临界阈值。此外，该项目将研究网络驱动数据收集的新形式，其中包括更多信息，以产生更有代表性的样本。经典的抽样结果不适用于网络驱动的抽样，因为朋友是相似的，导致样本之间的依赖。以往的理论结果表明，一些网络驱动的研究不能得到平方根n一致估计量。一项研究是否获得平方根n一致性取决于(i)底层社会网络的频谱特性和（ii）采样树的生长情况。本研究旨在提供校正样本间相关性的新估计器。这些依赖校正的估计器可以获得平方根n一致性，即使当前的估计器没有。该项目还将为网络驱动采样构建新的诊断和新的采样设计。新的光谱框架将提供一套理论、方法和实践，使研究能够获得平方根n一致的估计。

Probability sampling drastically reduces the burden of research in various disciplines because statistical inference can extend conclusions from a sample to the entire population. However, classical sampling techniques require a sampling frame that lists each individual in the population and a way of contacting each individual. In many settings, a sampling frame is not available. In others, a sampling frame is too expensive to compile or only covers a biased subset of the population. Particularly with hard-to-reach populations, network-driven sampling provides one of the only ways to find members of the population. Leveraging a network to find a target population appears in many disciplines with a multitude of names: respondent-driven sampling, snowball sampling, web crawling, link-tracing, breadth-first search, co-immunoprecipitation, and chromatin immunoprecipitation. These disparate techniques all provide access to hard-to-reach and networked populations by essentially asking participants to refer friends. As a result, these are all network-driven techniques. Classical sampling theory does not apply to network-driven sampling because friends are similar; this induces dependence between samples that is influenced by the underlying social network. Preliminary research conducted by the investigator identifies a critical threshold that relates the structure of the social network to the referral rate in the sampling tree; beyond this critical threshold, standard network-driven approaches produce highly uncertain estimates. This research aims to produce new statistical techniques that continue to perform well beyond the critical threshold. Moreover, this project will study novel forms of network-driven data collection that incorporate additional information to produce more representative samples. Classical sampling results are not applicable to network-driven sampling because friends are similar, inducing dependence between samples. Previous theoretical results show that some network-driven studies do not obtain square root n-consistent estimators. Whether a study obtains square root n-consistency depends on both (i) the spectral properties of the underlying social network and (ii) the growth of the sampling tree. This research aims to provide new estimators that correct for the dependence between samples. These dependence-corrected estimators can obtain square root n-consistency, even when current estimators do not. This project will also construct new diagnostics and new sampling designs for network-driven sampling. The new spectral framework will provide a suite of theory, methodology, and practices that will enable studies to obtain square root n-consistent estimators.