On Identifiability in Capture–Recapture Models |
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Authors: | Hajo Holzmann Axel Munk Walter Zucchini |
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Institution: | Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Maschmühlenweg 8-10, D–37073 Göttingen, Germany;Institut für Statistik und Ökonometrie, Platz der Göttinger Sieben 5, D–37073 Göttingen, Germany |
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Abstract: | Summary . We study the issue of identifiability of mixture models in the context of capture–recapture abundance estimation for closed populations. Such models are used to take account of individual heterogeneity in capture probabilities, but their validity was recently questioned by Link (2003, Biometrics 59, 1123–1130) on the basis of their nonidentifiability. We give a general criterion for identifiability of the mixing distribution, and apply it to establish identifiability within families of mixing distributions that are commonly used in this context, including finite and beta mixtures. Our analysis covers binomial and geometrically distributed outcomes. In an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models. |
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Keywords: | Abundance estimation Beta mixture Capture–recapture Finite mixture Heterogeneity Identifiability Uniform mixture |
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