title: On identifiability in capture-recapture models.
abstract: 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.
authors.affiliation: Institut für Mathematische Stochastik, Georg-August-Universität Göttingen, Maschmühlenweg 8-10, D-37073 Göttingen, Germany.
authors.forename: Hajo
authors.initials: H
authors.lastname: Holzmann
authors.forename: Axel
authors.initials: A
authors.lastname: Munk
authors.forename: Walter
authors.initials: W
authors.lastname: Zucchini
mesh_terms: D000818:Animals; D000835:Animals, Wild; D001699:Biometry / Q000379:methods*; D015233:Models, Statistical; D011157:Population Dynamics; D018709:Statistics, Nonparametric