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An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data

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  • Wen-Han Hwang
  • Richard Huggins

Abstract

Part of the folklore of capture-recapture experiments is that ignoring heterogeneity of capture probabilities results in a downward bias. This has been based on experience and simulation studies but is often interpreted as being due to individuals with lower capture probabilities. Here estimating equation arguments are used to show that the effect on Horvitz--Thompson-type estimators of ignoring heterogeneity in capture-recapture experiments is to introduce a downward bias. The arguments are extended to continuous-time experiments and to an influence function constructed to determine the effect of a small number of individuals with heterogeneous capture probabilities in an otherwise homogeneous population and the influence function is shown to be negative. The downward bias holds even if the small number of heterogeneous individuals have capture probabilities larger than the homogeneous majority, and this is confirmed by simulations. Copyright 2005, Oxford University Press.

Suggested Citation

  • Wen-Han Hwang & Richard Huggins, 2005. "An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data," Biometrika, Biometrika Trust, vol. 92(1), pages 229-233, March.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:229-233
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.229
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    Cited by:

    1. Olivier Binette & Rebecca C. Steorts, 2022. "On the reliability of multiple systems estimation for the quantification of modern slavery," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 640-676, April.
    2. Richard Huggins & Wen‐Han Hwang, 2007. "Non‐parametric estimation of population size from capture–recapture data when the capture probability depends on a covariate," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 429-443, August.
    3. Fodé Tounkara & Louis‐Paul Rivest, 2015. "Mixture regression models for closed population capture–recapture data," Biometrics, The International Biometric Society, vol. 71(3), pages 721-730, September.
    4. Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2019. "On the Turing estimator in capture–recapture count data under the geometric distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 149-172, March.
    5. Félix-Medina Martín Humberto, 2021. "Combining Cluster Sampling and Link-Tracing Sampling to Estimate Totals and Means of Hidden Populations in Presence of Heterogeneous Probabilities of Links," Journal of Official Statistics, Sciendo, vol. 37(4), pages 865-905, December.
    6. Kyle Vincent & Steve Thompson, 2017. "Estimating Population Size With Link-Tracing Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1286-1295, July.
    7. Wen-Han Hwang & Jakub Stoklosa & Ching-Yun Wang, 2022. "Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 303-320, June.
    8. Hannah Worthington & Rachel S. McCrea & Ruth King & Richard A. Griffiths, 2019. "Estimation of Population Size When Capture Probability Depends on Individual States," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 154-172, March.
    9. B. J. T. Morgan & M. S. Ridout, 2008. "A new mixture model for capture heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 433-446, September.

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