Lecture on "Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture datas"
Speaker: liu yu kun
Date：December 30, 2016
Time: 4:00 pm-5:30 pm
Location: The conference room on the second floor
Sponsor: School Of Statistici QFNU
Capture-recapture experiments are widely used to collect the capture-recapture data needed to estimate the abundance of a closed population. To account for the observable heterogeneity in the capture probabilities, Alho (1990) proposed a semiparametric model in which the capture probabilities are modelled by a parametric model and the distribution of individual characteristics is left unspecied. A conditional likelihood method was then proposed to obtain point estimates and Wald-type condence 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 condence intervals with lower limits that are less than the number of captured individuals or even negative. In this paper, we propose a full empirical likelihood approach based on Alho (1990)'s model. We show that the empirical likelihood ratio for the abundance is asymptotically chi-square with one degree of freedom. Simulation studies show that the empirical-likelihood-based method is superior to the conditional-likelihood-based method: the empirical likelihood ratio based condence interval has much better coverage, and the maximum empirical likelihood estimator has a smaller mean square error. We analyze three real data sets to illustrate the advantages of the proposed empirical likelihood method.