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Wen-Han Hwang, Richard Huggins, An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data, Biometrika, Volume 92, Issue 1, March 2005, Pages 229–233, https://doi.org/10.1093/biomet/92.1.229
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Abstract
Part of the folklore of capture-recapture experiments is that ignoring heterogeneity of capture probabilities results in a downward bias. This has been based on experience and simulation studies but is often interpreted as being due to individuals with lower capture probabilities. Here estimating equation arguments are used to show that the effect on Horvitz–Thompson-type estimators of ignoring heterogeneity in capture-recapture experiments is to introduce a downward bias. The arguments are extended to continuous-time experiments and to an influence function constructed to determine the effect of a small number of individuals with heterogeneous capture probabilities in an otherwise homogeneous population and the influence function is shown to be negative. The downward bias holds even if the small number of heterogeneous individuals have capture probabilities larger than the homogeneous majority, and this is confirmed by simulations.
