Consistent Least Squares Estimation in Population-Size-Dependent Branching Processes

• 成果类型: Article
• 署名作者: Braunsteins, Peter; Hautphenne, Sophie; Minuesa, Carmen
• 署名单位: University of New South Wales Sydney; University of Melbourne
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2571247
• 发表日期: 2026-04-03
• 页码: 1695-1707
• 关键词: Almost sure extinction; Carrying capacity; inference

摘要

We derive the first conditionally consistent estimators for a class of parametric Markov population models with logistic growth, which are suitable for modeling endangered populations in restricted habitats with a carrying capacity. We focus on discrete-time parametric population-size-dependent branching processes, for which we propose a new class of weighted least-squares estimators based on a single trajectory of population size counts. We establish the consistency and asymptotic normality of our estimators, conditional on non-extinction up to time n, as n ->infinity. Since Markov population models with a carrying capacity become extinct almost surely under general conditions, our proofs rely on arguments distinct from those in the existing literature. Our results are motivated by conservation biology, where endangered populations are often studied precisely because they are still alive, leading to an observation bias. Through simulated examples, we show that our conditionally consistent estimators generally reduce this bias for key quantities such as a habitat's carrying capacity. We apply our methodology to estimate the carrying capacity of the Chatham Island black robin, a population reduced to a single breeding female in the 1970's, which has since recovered but has yet to reach the island's carrying capacity. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.