标题： 两步半参数经验似然推断来自具有缺失协变量的捕捉-再捕获数据 显示英文标题

标题： Two-step semiparametric empirical likelihood inference from capture-recapture data with missing covariates

摘要： 缺失的协变量在捕捉-再捕获研究中并不少见。 当捕捉-再捕获数据中的协变量信息是随机缺失时，已经证明了一种经验全似然方法在种群数量估计中优于基于条件似然的方法。 然而，完全观测的协变量必须是离散的，该方法不能直接应用于连续时间的捕捉-再捕获数据。 基于二项式和泊松回归模型，我们提出了一种两步半参数经验似然方法，在存在缺失协变量的情况下进行种群数量估计，无论完全观测的协变量是离散还是连续的。 我们证明了潜在参数和种群数量的最大半参数经验似然估计量是渐近正态的，并且比一个完全已知无缺失概率的情况下的对应估计量更有效。 经过缩放后，种群数量的经验似然比检验统计量服从自由度为1的极限卡方分布。 所提出的方法进一步扩展到一个膨胀计数回归模型，并构建了一个类似得分的检验来评估捕获次数中是否存在一个膨胀。 我们的模拟显示，与之前的方法相比，所提出的方法不仅在校正偏差方面表现更好，而且在存在完全观测连续协变量的情况下具有更准确的覆盖率，尽管当完全观测的协变量仅为离散时可能会有轻微的效率损失。 新方法的性能通过对香港莺的数据分析进行了说明。 显示英文摘要

摘要： Missing covariates are not uncommon in capture-recapture studies. When covariate information is missing at random in capture-recapture data, an empirical full likelihood method has been demonstrated to outperform conditional-likelihood-based methods in abundance estimation. However, the fully observed covariates must be discrete, and the method is not directly applicable to continuous-time capture-recapture data. Based on the Binomial and Poisson regression models, we propose a two-step semiparametric empirical likelihood approach for abundance estimation in the presence of missing covariates, regardless of whether the fully observed covariates are discrete or continuous. We show that the maximum semiparametric empirical likelihood estimators for the underlying parameters and the abundance are asymptotically normal, and more efficient than the counterpart for a completely known non-missingness probability. After scaling, the empirical likelihood ratio test statistic for abundance follows a limiting chi-square distribution with one degree of freedom. The proposed approach is further extended to one-inflated count regression models, and a score-like test is constructed to assess whether one-inflation exists among the number of captures. Our simulation shows that, compared with the previous method, the proposed method not only performs better in correcting bias, but also has a more accurate coverage in the presence of fully observed continuous covariates, although there may be a slight efficiency loss when the fully observed covariates are only discrete. The performance of the new method is illustrated by an analysis of the Hong Kong prinia data.