KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, P. R. China.
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada.
Biom J. 2022 Aug;64(6):1040-1055. doi: 10.1002/bimj.202100231. Epub 2022 Apr 15.
Abundance estimation from capture-recapture data is of great importance in many disciplines. Analysis of capture-recapture data is often complicated by the existence of one-inflation and heterogeneity problems. Simultaneously taking these issues into account, existing abundance estimation methods are usually constructed on the basis of conditional likelihood under one-inflated zero-truncated count models. However, the resulting Horvitz-Thompson-type estimators may be unstable, and the resulting Wald-type confidence intervals may exhibit severe undercoverage. In this paper, we propose a semiparametric empirical likelihood (EL) approach to abundance estimation under one-inflated binomial and Poisson regression models. To facilitate the computation of the EL method, we develop an expectation-maximization algorithm. We also propose a new score test for the existence of one-inflation and prove its asymptotic normality. Our simulation studies indicate that compared with existing estimators, the proposed score test is more powerful and the maximum EL estimator has a smaller mean square error. The advantages of our approaches are further demonstrated by analyses of prinia data from Hong Kong and drug user data from Bangkok.
丰度估计从捕获-再捕获数据在许多学科中都具有重要意义。捕获-再捕获数据分析通常由于存在一膨胀和异质性问题而变得复杂。同时考虑到这些问题，现有的丰度估计方法通常是基于一膨胀零截断计数模型下的条件似然构建的。然而，由此产生的霍维茨-汤普森型估计量可能不稳定，由此产生的 Wald 型置信区间可能表现出严重的低估。在本文中，我们提出了一种半参数经验似然 (EL) 方法，用于一膨胀二项式和泊松回归模型下的丰度估计。为了便于计算 EL 方法，我们开发了一种期望最大化算法。我们还提出了一种用于检测一膨胀存在的新得分检验，并证明了其渐近正态性。我们的模拟研究表明，与现有的估计量相比，所提出的得分检验更有效，最大 EL 估计量的均方误差更小。我们的方法的优势通过对来自香港的 prinia 数据和来自曼谷的吸毒者数据的分析进一步得到证明。
