Capture–recapture estimation based upon the geometric distribution allowing for heterogeneity

Sa-aat Niwitpong (), Dankmar Böhning (), Peter Heijden () and Heinz Holling ()

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 4, 495-519

Abstract: Capture–Recapture methods aim to estimate the size of an elusive target population. Each member of the target population carries a count of identifications by some identifying mechanism—the number of times it has been identified during the observational period. Only positive counts are observed and inference needs to be based on the observed count distribution. A widely used assumption for the count distribution is a Poisson mixture. If the mixing distribution can be described by an exponential density, the geometric distribution arises as the marginal. This note discusses population size estimation on the basis of the zero-truncated geometric (a geometric again itself). In addition, population heterogeneity is considered for the geometric. Chao’s estimator is developed for the mixture of geometric distributions and provides a lower bound estimator which is valid under arbitrary mixing on the parameter of the geometric. However, Chao’s estimator is also known for its relatively large variance (if compared to the maximum likelihood estimator). Another estimator based on a censored geometric likelihood is suggested which uses the entire sample information but is less affected by model misspecifications. Simulation studies illustrate that the proposed censored estimator comprises a good compromise between the maximum likelihood estimator and Chao’s estimator, e.g. between efficiency and bias. Copyright Springer-Verlag 2013

Keywords: Capture-recapture; Chao’s estimator; Censored estimator; Censored likelihood; Estimation under model misspecification; Truncated likelihood (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00184-012-0401-0

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