Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture data

• 成果类型: Article
• 署名作者: Liu, Yukun; Li, Pengfei; Qin, Jing
• 署名单位: East China Normal University; University of Waterloo; National Institutes of Health (NIH) - USA; NIH National Institute of Allergy & Infectious Diseases (NIAID)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx038
• 发表日期: 2017
• 页码: 527543
• 关键词: models; size; covariate

摘要

Capture-recapture experiments are widely used to collect data needed for estimating the abundance of a closed population. To account for heterogeneity in the capture probabilities, Huggins (1989) and Alho (1990) proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified. A conditional likelihood method was then proposed to obtain point estimates andWald-type confidence intervals for the abundance. Empirical studies show that the small-sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right, which may produceWald-type confidence intervals with lower limits that are less than the number of captured individuals or even are negative. In this paper, we propose a full empirical likelihood approach based on Huggins andAlho's model. We showthat the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi-squared with one degree of freedom, and that the maximum empirical likelihood estimator achieves semiparametric efficiency. Simulation studies show that the empirical likelihood-based method is superior to the conditional likelihood-based method: its confidence interval has much better coverage, and the maximum empirical likelihood estimator has a smaller mean square error. We analyse three datasets to illustrate the advantages of our empirical likelihood approach.