Estimating the size of hard-to-reach populations is an important problem for many fields. The Network Scale-up Method (NSUM) is a relatively new approach to estimate the size of these hard-to-reach populations by asking respondents the question, "How many X's do you know," where X is the population of interest (e.g. "How many female sex workers do you know?"). The answers to these questions form Aggregated Relational Data (ARD). The NSUM has been used to estimate the size of a variety of subpopulations, including female sex workers, drug users, and even children who have been hospitalized for choking. Within the Network Scale-up methodology, there are a multitude of estimators for the size of the hidden population, including direct estimators, maximum likelihood estimators, and Bayesian estimators. In this article, we first provide an in-depth analysis of ARD properties and the techniques to collect the data. Then, we comprehensively review different estimation methods in terms of the assumptions behind each model, the relationships between the estimators, and the practical considerations of implementing the methods. Finally, we provide a summary of the dominant methods and an extensive list of the applications, and discuss the open problems and potential research directions in this area.

翻译：估计难以接触的人口规模是许多领域的一个重要问题。 网络扩大方法(NSUM)是一个相对较新的方法,用来估计这些难以接触的人口的规模。 它向答卷人询问“你知道有多少X's,你知道有多少X's,”X是感兴趣的人口(例如“有多少女性性工作者?”)。 这些问题的答案是综合关系数据(ARD)。 国家扩大方法(NSUM)被用来估计各种亚人口的规模,包括女性性工作者、吸毒者,甚至因窒息而住院的儿童。 在网络扩大方法中,对隐蔽人口的规模有许多估计者,包括直接估计者、最大可能性估计者以及Bayesian估计者。 在文章中,我们首先深入分析了ARA的特性和收集数据的技术。 然后,我们从每种模型的假设、估计者之间的关系以及广泛应用方法的实际考虑的角度,全面审视了各种估计方法的假设方法。 最后,我们提供了这一研究方法的概况和广泛应用领域。