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Post-seminar Q&A: Graduate students are invited to stay after the seminar for a Q&A with the speaker (~12pm–12:10pm).
Abstract: Capture-recapture experiments are widely used to collect data needed to estimate 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 negative. Furthermore, the conditional-likelihood method may produce spuriously large estimates when a nontrivial number of capture probabilities are close to 0.
In this talk, we present a penalized empirical likelihood approach based on Huggins and Alho's model. We show that the null distribution of the penalized empirical likelihood ratio for the abundance is asymptotically chi-square with one degree of freedom, and the maximum penalized empirical likelihood estimator achieves semiparametric efficiency. We further propose an expectation–maximization algorithm to numerically calculate the proposed point estimate and penalized empirical likelihood ratio function. Simulation studies show that the penalized-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.