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Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments

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  • Marco Alfò
  • Dankmar Böhning
  • Irene Rocchetti

Abstract

Capture‐recapture studies have attracted a lot of attention over the past few decades, especially in applied disciplines where a direct estimate for the size of a population of interest is not available. Epidemiology, ecology, public health, and biodiversity are just a few examples. The estimation of the number of unseen units has been a challenge for theoretical statisticians, and considerable progress has been made in providing lower bound estimators for the population size. In fact, it is well known that consistent estimators for this cannot be provided in the very general case. Considering a case where capture‐recapture studies are summarized by a frequency of frequencies distribution, we derive a simple upper bound of the population size based on the cumulative distribution function. We introduce two estimators of this bound, without any specific parametric assumption on the distribution of the observed frequency counts. The behavior of the proposed estimators is investigated using several benchmark datasets and a large‐scale simulation experiment based on the scheme discussed by Pledger.

Suggested Citation

  • Marco Alfò & Dankmar Böhning & Irene Rocchetti, 2021. "Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments," Biometrics, The International Biometric Society, vol. 77(1), pages 237-248, March.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:1:p:237-248
    DOI: 10.1111/biom.13265
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    1. repec:bla:jorssc:v:57:y:2008:i:1:p:89-102 is not listed on IDEAS
    2. Alessio Farcomeni & Luca Tardella, 2010. "Reference Bayesian methods for recapture models with heterogeneity," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 187-208, May.
    3. Lanumteang, K. & Böhning, D., 2011. "An extension of Chao's estimator of population size based on the first three capture frequency counts," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2302-2311, July.
    4. Ruth King & Sheila M. Bird & Antony M. Overstall & Gordon Hay & Sharon J. Hutchinson, 2014. "Estimating prevalence of injecting drug users and associated heroin-related death rates in England by using regional data and incorporating prior information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 209-236, January.
    5. William A. Link, 2003. "Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 59(4), pages 1123-1130, December.
    6. Chris J. Lloyd & Donald J. Frommer, 2004. "Regression‐based estimation of the false negative fraction when multiple negatives are unverified," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 619-631, November.
    7. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    8. Shirley Pledger, 2005. "The Performance of Mixture Models in Heterogeneous Closed Population Capture–Recapture," Biometrics, The International Biometric Society, vol. 61(3), pages 868-873, September.
    9. Xuan Mao, Chang, 2007. "Estimating population sizes for capture-recapture sampling with binomial mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5211-5219, July.
    10. Metin I Eren & Anne Chao & Wen-Han Hwang & Robert K Colwell, 2012. "Estimating the Richness of a Population When the Maximum Number of Classes Is Fixed: A Nonparametric Solution to an Archaeological Problem," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-11, May.
    11. Peter G.M. Van Der Heijden & Maarten Cruyff & Hans C. Van Houwelingen, 2003. "Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 289-304, August.
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    Cited by:

    1. Yang Liu & Rong Kuang & Guanfu Liu, 2024. "Penalized likelihood inference for the finite mixture of Poisson distributions from capture-recapture data," Statistical Papers, Springer, vol. 65(5), pages 2751-2773, July.

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