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

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.

Keywords:

• Capture-recapture
• heterogeneity
• identifiability
• mixture model
• population Size

Notes

1 Sanathanan (1972, 1977) proves that the conditional and uncondtional mle’s are asymptotic equivalent.

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. “José Galvão Leite” gratefully acknowledge the scolarship ‘Professor Visitante Nacional Senior (PVNS)’ provided by CAPES.