A note on identifiability and maximum likelihood estimation for a heterogeneous capture-recapture model

George Lucas Moraes Pezzott, Luis Ernesto Bueno Salasar, José Galvão Leite and Francisco Louzada-Neto

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 21, 5273-5293

Abstract: This article discusses identifiability and maximum likelihood estimation for a closed population capture-recapture model with heterogeneity in capture probabilities. The model assumes that the individual capture probabilities arise from a discrete distribution over the interval (0,1]. Considering the complete likelihood, without applying any conditioning, we prove that identifiability holds under a restriction on the number of support points of the mixing distribution. Under this identifiability assumption, we present a simple closed-form iterative algorithm for maximum likelihood estimation. Interval estimation is carried by a bootstrap resampling procedure. The proposed methods are illustrated on a literature real data set and a simulation study is carried to assess the frequentist merits of different population size estimators.

Date: 2020
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DOI: 10.1080/03610926.2019.1615628

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