Minimum chi-square method for estimating population size in capture-recapture experiments

Closed population capture-recapture estimation of population size is difficult under heterogeneous capture probabilities. We introduce the minimum chi-square method which can handle multi-occasion capture-recapture data. It complements likelihood methods with elements that can lead to confidence intervals and assessment of goodness-of-fit. We conduct a comprehensive study on the minimum chi-square method for estimating the size of a closed population using multiple-occasion capture-recapture data under heterogeneous capture probability. We also develop two different bootstrap techniques that can be combined with any underlying estimator, be it the minimum chi-square estimator or a likelihood estimator, to perform useful inference for estimating population size. We present a simulation study on the minimum chi-square method and apply it to analyze white stork multiple capture-recapture data. Under certain conditions, the chi-square method outperforms the likelihood based methods.