Note on nonparametric inference for capture-recapture experiments with heterogeneous capture probabilities

The estimation of the size of a population using capture-recapture data if the capture probabilities are heterogeneous is essentially an unsolved problem in that no nonparametric estimator has been shown to be uniformly applicable. Moreover, often the conditions under which the various nonparametric estimators give reasonable estimates axe either unknown or uncheckable. Here a feasible nonpaxametric extension of a parametric empirical Bayes method used by Huggins (2001) is examined. It is concluded that assumptions concerning the distribution of the capture probabilities are required to successfully estimate the population size. A byproduct of the procedure is a conditional likelihood based test for time dependent capture probabilities in the presence of heterogeneous capture probabilities.