Full likelihood inference for abundance from continuous time capture-recapture data

Capture-recapture experiments are widely used cost-effective sampling techniques for estimating population sizes or abundances in biology, ecology, demography, epidemiology and reliability studies. For continuous time capture-recapture data, existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation. The corresponding Wald-type confidence intervals for the abundance may have severe undercoverage, and their lower limits can be below the number of individuals captured. We propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood. Under both parametric and semiparametric intensity models, we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically (2) with 1 degree of freedom. Simulations indicate that compared with conditional-likelihood-based methods, the maximum full likelihood estimator has a smaller mean-square error, and the likelihood ratio confidence intervals often have remarkable gains in coverage probability. We illustrate the advantages of the proposed approach by analysing illegal immigrant data for the Netherlands and Prinia flaviventris data from Hong Kong.