A martingale estimating equation for a capture-recapture experiment in discrete time

Abstract

We use martingale theory and a method-of-moments technique to derive a class of estimators for the size of a closed population in a capture-recapture experiment in discrete time where the capture probabilities on the successive capture occasions are allowed to be different. The same capture probability is assumed to apply to all animals in the population on the same occasion. Explicit expressions are given for these estimators and their associated standard errors which involve only simple computation. An optimal estimator for the population size is found. Asymptotic results are readily obtained by an application of a martingale central limit theorem. Two examples are given to compare the results.