Electronic Journal of Statistics

Identifiability and inferential issues in capture-recapture experiments with heterogeneous detection probabilities

Alessio Farcomeni and Luca Tardella

Full-text: Open access

Abstract

We focus on a capture-recapture model in which capture probabilities arise from an unspecified distribution $F$. We show that model parameters are identifiable based on the unconditional likelihood. This is not true with the conditional likelihood. We also clarify that consistency and asymptotic equivalence of maximum likelihood estimators based on conditional and unconditional likelihood do not hold. We show that estimates of the undetected fraction of population based on the unconditional likelihood converge to the so-called estimable sharpest lower bound and we derive a new asymptotic equivalence result. We finally provide theoretical and simulation arguments in favor of the use of the unconditional likelihood rather than the conditional likelihood especially when one is willing to infer on the sharpest lower bound.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 2602-2626.

Dates
First available in Project Euclid: 11 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1357913090

Digital Object Identifier
doi:10.1214/12-EJS758

Mathematical Reviews number (MathSciNet)
MR3020278

Zentralblatt MATH identifier
1302.62099

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Binomial mixture capture-recapture identifiability conditional likelihood complete likelihood unconditional likelihood

Citation

Farcomeni, Alessio; Tardella, Luca. Identifiability and inferential issues in capture-recapture experiments with heterogeneous detection probabilities. Electron. J. Statist. 6 (2012), 2602--2626. doi:10.1214/12-EJS758. https://projecteuclid.org/euclid.ejs/1357913090


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