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


Niwitpong, Sa-aat, Böhning, Dankmar, van der Heijden, Peter G.M. and Holling, Heinz (2012) Capture-recapture estimation based upon the geometric distribution allowing for heterogeneity. Metrika, 76, 495-519. (doi:10.1007/s00184-012-0401-0).

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Description/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.

Item Type: Article
ISSNs: 0026-1335 (print)
1435-926X (electronic)
Keywords: capture-recapture, chao’s estimator, censored estimator, censored likelihood, estimation under model misspecification, truncated likelihood
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Divisions: Faculty of Medicine > Primary Care and Population Sciences
Faculty of Social and Human Sciences > Mathematical Sciences > Statistics
Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute
ePrint ID: 341869
Date Deposited: 07 Aug 2012 10:35
Last Modified: 27 Mar 2014 20:24
URI: http://eprints.soton.ac.uk/id/eprint/341869

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