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A modification of Chao's lower bound estimator in the case of one-inflation

A modification of Chao's lower bound estimator in the case of one-inflation
A modification of Chao's lower bound estimator in the case of one-inflation

For zero-truncated count data, as they typically arise in capture-recapture modelling, the nonparametric lower bound estimator of Chao is a frequently used estimator of population size. It is a simple, nonparametric estimator involving only counts of one and counts of two. The estimator is asymptotically unbiased if the count distribution is a member of the power series family and is providing a lower bound estimator if the distribution is a mixture of a member of the power series family. However, if there is one-inflation Chao’s estimator can severely overestimate as we show here. This is also illustrated by routinely collected country-wide data on family violence in the Netherlands. A new lower bound estimator is developed which involves only counts of twos and threes, thus avoiding the overestimation caused by one-inflation. We show that the new estimator is asymptotically unbiased for a power series distribution with and without one-inflation and provides a lower bound estimator under a mixture of power series distributions with and without one-inflation. For all estimators bias-adjusted versions are developed that reduce the bias considerably when the sample size is small. A simulation study compares the modified Chao estimator with the conventional estimator as well as with an estimator suggested by Chiu and Chao more recently.

Behavioral response, Bias reduction, Capture-recapture, Mixture model, Nonparametric estimator of population size, Power series distribution
1-24
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Kaskasamkul, Panicha
764f5d81-4b4a-41ad-a35c-f55abcf19e19
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612
Böhning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Kaskasamkul, Panicha
764f5d81-4b4a-41ad-a35c-f55abcf19e19
van der Heijden, Peter G.M.
85157917-3b33-4683-81be-713f987fd612

Böhning, Dankmar, Kaskasamkul, Panicha and van der Heijden, Peter G.M. (2018) A modification of Chao's lower bound estimator in the case of one-inflation. Metrika, 1-24. (doi:10.1007/s00184-018-0689-5).

Record type: Article

Abstract

For zero-truncated count data, as they typically arise in capture-recapture modelling, the nonparametric lower bound estimator of Chao is a frequently used estimator of population size. It is a simple, nonparametric estimator involving only counts of one and counts of two. The estimator is asymptotically unbiased if the count distribution is a member of the power series family and is providing a lower bound estimator if the distribution is a mixture of a member of the power series family. However, if there is one-inflation Chao’s estimator can severely overestimate as we show here. This is also illustrated by routinely collected country-wide data on family violence in the Netherlands. A new lower bound estimator is developed which involves only counts of twos and threes, thus avoiding the overestimation caused by one-inflation. We show that the new estimator is asymptotically unbiased for a power series distribution with and without one-inflation and provides a lower bound estimator under a mixture of power series distributions with and without one-inflation. For all estimators bias-adjusted versions are developed that reduce the bias considerably when the sample size is small. A simulation study compares the modified Chao estimator with the conventional estimator as well as with an estimator suggested by Chiu and Chao more recently.

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Chao One Metrika R2 - Accepted Manuscript
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Böhning 2018 Article A Modification of Chaos Lower Bound - Version of Record
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More information

Accepted/In Press date: 20 September 2018
e-pub ahead of print date: 3 October 2018
Keywords: Behavioral response, Bias reduction, Capture-recapture, Mixture model, Nonparametric estimator of population size, Power series distribution

Identifiers

Local EPrints ID: 423450
URI: https://eprints.soton.ac.uk/id/eprint/423450
PURE UUID: 5dbc00b5-54fe-4402-b122-88f7d51b435f
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: 24 Sep 2018 16:30
Last modified: 10 Dec 2019 01:38

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