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

Capture-recapture estimation based upon the geometric distribution allowing for heterogeneity
Capture-recapture estimation based upon the geometric distribution allowing for heterogeneity
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.
capture-recapture, chao’s estimator, censored estimator, censored likelihood, estimation under model misspecification, truncated likelihood
495-519
Niwitpong, Sa-aat
f5bf8776-4843-4e5d-9b71-6bc8f8d122db
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Holling, Heinz
88d46f56-77ca-4d0e-b035-a51aff735435
Niwitpong, Sa-aat
f5bf8776-4843-4e5d-9b71-6bc8f8d122db
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Holling, Heinz
88d46f56-77ca-4d0e-b035-a51aff735435

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 (4), 495-519. (doi:10.1007/s00184-012-0401-0).

Record type: Article

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.

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More information

Published date: 27 July 2012
Keywords: capture-recapture, chao’s estimator, censored estimator, censored likelihood, estimation under model misspecification, truncated likelihood
Organisations: Statistics, Statistical Sciences Research Institute, Primary Care & Population Sciences

Identifiers

Local EPrints ID: 341869
URI: http://eprints.soton.ac.uk/id/eprint/341869
PURE UUID: cbd7f18f-cc4a-4fc8-8560-1770d5dacb72
ORCID for Dankmar Böhning: ORCID iD orcid.org/0000-0003-0638-7106
ORCID for Peter G.M. van der Heijden: ORCID iD orcid.org/0000-0002-3345-096X

Catalogue record

Date deposited: 07 Aug 2012 10:35
Last modified: 09 Nov 2021 03:29

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Contributors

Author: Sa-aat Niwitpong
Author: Heinz Holling

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