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

SummaryCapture-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 and Wald-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 produce Wald-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 and Alho’s model. We show that 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.