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

Dankmar Böhning (), Panicha Kaskasamkul () and Peter G. M. Heijden ()
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Dankmar Böhning: University of Southampton
Panicha Kaskasamkul: Naresuan University
Peter G. M. Heijden: University of Southampton

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 3, No 4, 384 pages

Abstract: 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.

Keywords: Capture-recapture; Behavioral response; Power series distribution; Nonparametric estimator of population size; Mixture model; Bias reduction (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-018-0689-5

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