Some general comparative points on Chao’s and Zelterman’s estimators of population size
Some general comparative points on Chao’s and Zelterman’s estimators of population size
Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study
221-236
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
June 2010
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Böhning, Dankmar
(2010)
Some general comparative points on Chao’s and Zelterman’s estimators of population size.
Scandinavian Journal of Statistics, 37 (2), .
(doi:10.1111/j.1467-9469.2009.00676.x).
Abstract
Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study
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e-pub ahead of print date: 19 January 2010
Published date: June 2010
Organisations:
Statistical Sciences Research Institute, Pure Mathematics
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Local EPrints ID: 210459
URI: http://eprints.soton.ac.uk/id/eprint/210459
ISSN: 0303-6898
PURE UUID: a24878a9-c7fd-468e-b6e7-d8e1e2d7e480
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Date deposited: 09 Feb 2012 11:24
Last modified: 15 Mar 2024 03:39
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