标题： 在协变量随机缺失的情况下，从捕捉-再捕捉数据中进行最大似然丰度估计 显示英文标题

标题： Maximum likelihood abundance estimation from capture-recapture data when covariates are missing at random

摘要： 在捕捉-再捕捉实验中，个体协变量可能会缺失，尤其是在被捕捉次数较少时。 当协变量信息是随机缺失时，逆概率加权方法和多重插补方法被广泛用于获得种群数量的点估计量。 然后这些点估计量被用来构建种群数量的Wald型置信区间。 然而，这样的区间可能具有严重不准确的覆盖概率，其下限甚至可能小于曾经被捕捉到的个体数量。 在本文中，我们提出了在存在缺失协变量的情况下对种群数量的最大经验似然估计方法。 我们证明了最大经验似然估计量是渐近正态的，并且种群数量的经验似然比统计量服从自由度为1的卡方极限分布。 模拟结果表明，所提出的估计量比现有的估计量具有更小的均方误差，所提出的经验似然比置信区间通常比现有的Wald型置信区间具有更准确的覆盖概率。 我们通过分析在香港收集的黄腹柳莺物种来说明所提出的方法。 显示英文摘要

摘要： In capture-recapture experiments, individual covariates may be subject to missing, especially when the number of times of being captured is small. When the covariate information is missing at random, the inverse probability weighting method and multiple imputation method are widely used to obtain the point estimators of the abundance. These point estimators are then used to construct the Wald-type confidence intervals for the abundance. However, such intervals may have severely inaccurate coverage probabilities and their lower limits can be even less than the number of individuals ever captured. In this paper, we proposed a maximum empirical likelihood estimation approach for the abundance in presence of missing covariates. We show that the maximum empirical likelihood estimator is asymptotically normal, and that the empirical likelihood ratio statistic for abundance has a chisquare limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has smaller mean square error than the existing estimators, and the proposed empirical likelihood ratio confidence interval usually has more accurate coverage probabilities than the existing Wald-type confidence intervals. We illustrate the proposed method by analyzing the bird species yellow-bellied prinia collected in Hong Kong.