论文标题
一致的最小二乘估计在人口大小的分支过程中
Consistent least squares estimation in population-size-dependent branching processes
论文作者
论文摘要
我们为具有逻辑生长的一类参数马尔可夫人群模型的第一个有条件的一致估计量提供，这适用于具有承载能力的受限制栖息地中的濒危种群。我们专注于离散的参数群体依赖性分支过程，为此我们提出了基于单个种群数量计数的单个轨迹的新的加权最小二乘估计器。我们建立了估计器的一致性和渐近正态性，以$ n $的时间为条件，为$ n \ to \ infty $。由于马尔可夫人口模型在一般条件下几乎肯定会灭绝，因此我们的证据依赖于与现有文献不同的论点。 我们的结果是由保护生物学的动机，在这种生物学上，经常研究濒危人群，因为它们仍然活着，导致观察偏见。通过模拟示例，我们表明，条件一致的估计器通常会减少关键数量（例如栖息地的承载能力）的偏见。我们运用我们的方法来估计查塔姆岛黑罗宾的承载能力，该人口在1970年代减少到一个繁殖女性，此后恢复了，但尚未达到该岛的承载能力。
We derive the first conditionally consistent estimators for a class of parametric Markov population models with logistic growth, which are suitable for modelling 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 $n\to\infty$. 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.
