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

Author

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

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.

Suggested Citation

  • George Lucas Moraes Pezzott & Luis Ernesto Bueno Salasar & José Galvão Leite & Francisco Louzada-Neto, 2020. "A note on identifiability and maximum likelihood estimation for a heterogeneous capture-recapture model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(21), pages 5273-5293, November.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:21:p:5273-5293
    DOI: 10.1080/03610926.2019.1615628
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