Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Rome, Italy.
Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK.
Biometrics. 2021 Mar;77(1):237-248. doi: 10.1111/biom.13265. Epub 2020 Apr 29.
Capture-recapture studies have attracted a lot of attention over the past few decades, especially in applied disciplines where a direct estimate for the size of a population of interest is not available. Epidemiology, ecology, public health, and biodiversity are just a few examples. The estimation of the number of unseen units has been a challenge for theoretical statisticians, and considerable progress has been made in providing lower bound estimators for the population size. In fact, it is well known that consistent estimators for this cannot be provided in the very general case. Considering a case where capture-recapture studies are summarized by a frequency of frequencies distribution, we derive a simple upper bound of the population size based on the cumulative distribution function. We introduce two estimators of this bound, without any specific parametric assumption on the distribution of the observed frequency counts. The behavior of the proposed estimators is investigated using several benchmark datasets and a large-scale simulation experiment based on the scheme discussed by Pledger.
在过去几十年中，捕获-再捕获研究引起了很多关注，特别是在那些无法直接估计感兴趣的总体大小的应用学科中。流行病学、生态学、公共卫生和生物多样性只是其中的几个例子。对未观察到的单位数量的估计一直是理论统计学家面临的挑战，并且在提供总体大小的下界估计方面已经取得了相当大的进展。事实上，众所周知，在非常一般的情况下，不能为这种情况提供一致的估计。考虑到捕获-再捕获研究由频率分布频率总结的情况，我们根据累积分布函数推导出总体大小的简单上限。我们引入了该上限的两个估计量，而对观测频率计数的分布没有任何特定的参数假设。使用几个基准数据集和基于 Pledger 讨论的方案进行的大规模模拟实验，研究了所提出的估计量的行为。
