Focused information criterion for capture re-capture models for closed populations

We propose a criterion for selecting a capture-recapture model for closed populations which follows the basic idea of the Focused Information Criterion (FIC) of Claeskens and Hjort. The proposed criterion aims at selecting the model which, among the available models, leads to the smallest Mean Squared Error (MSE) of the resulting estimator of the population size and is based on an index which, up to a constant term, is equal to the asymptotic MSE of the estimator. Two alternative approaches to estimate this FIC index are proposed. We also deal with multimodel inference; in this case, the population size is estimated by using a weighted average of the estimates coming from different models, with weights chosen as to minimize the MSE of the resulting estimator. The proposed model selection approach is compared with more common approaches through a series of simulations. It is also illustrated by an application based on a dataset coming from a live-trapping experiment.