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On the Nonidentifiability of Population Sizes

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  • Chang Xuan Mao

Abstract

Summary When a nonparametric mixture model is adopted to deal with the heterogeneity among individual capture probabilities, the population size is nonidentifiable (Link, 2003, Biometrics59, 1123–1130). Holzmann, Munk, and Zucchini (2006, Biometrics62, 934–936) discussed the conditions under which a subfamily of mixing distributions is identifiable. Link (2006, Biometrics92, 936–939) found that the nonidentifiability occurs across identifiable subfamilies. It is shown that there is a subfamily in which each mixing distribution is determined by its mixture, and the population size admits estimable lower bounds that can be used to construct lower confidence limits.

Suggested Citation

  • Chang Xuan Mao, 2008. "On the Nonidentifiability of Population Sizes," Biometrics, The International Biometric Society, vol. 64(3), pages 977-979, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:977-979
    DOI: 10.1111/j.1541-0420.2008.01078.x
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    References listed on IDEAS

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    1. 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.
    2. Hajo Holzmann & Axel Munk & Walter Zucchini, 2006. "On Identifiability in Capture–Recapture Models," Biometrics, The International Biometric Society, vol. 62(3), pages 934-936, September.
    3. 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.
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    Cited by:

    1. Chang Xuan Mao & Ruochen Huang & Sijia Zhang, 2017. "Petersen estimator, Chapman adjustment, list effects, and heterogeneity," Biometrics, The International Biometric Society, vol. 73(1), pages 167-173, March.
    2. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    3. Chang Xuan Mao & Cuiying Yang & Yitong Yang & Wei Zhuang, 2017. "Estimating population sizes with the Rasch model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 705-716, June.
    4. Shirley Pledger & Kenneth H. Pollock & James L. Norris, 2010. "Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model," Biometrics, The International Biometric Society, vol. 66(3), pages 883-890, September.

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