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.

Automated summary

In this study, we introduce a new minimum chi-square method for estimating the size of a closed population using capture-recapture data. This method performs better than traditional likelihood methods under heterogeneous capture probabilities. Additionally, we develop two different bootstrap techniques that can be used with any underlying estimator for inferring population size.