IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v64y2008i3p977-979.html
   My bibliography  Save this article

On the Nonidentifiability of Population Sizes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1541-0420.2008.01078.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1541-0420.2008.01078.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chang Xuan Mao & Na You, 2009. "On Comparison of Mixture Models for Closed Population Capture–Recapture Studies," Biometrics, The International Biometric Society, vol. 65(2), pages 547-553, June.
    2. 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.
    3. Hajo Holzmann & Axel Munk, 2008. "The authors replied as follows:," Biometrics, The International Biometric Society, vol. 64(3), pages 979-981, September.
    4. William A. Link, 2006. "The author replied as follows:," Biometrics, The International Biometric Society, vol. 62(3), pages 936-939, September.
    5. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    6. 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.
    7. 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.
    8. Jakub Stoklosa & Wen-Han Hwang & Sheng-Hai Wu & Richard Huggins, 2011. "Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations," Biometrics, The International Biometric Society, vol. 67(4), pages 1659-1665, December.
    9. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.
    10. Dankmar Böhning & Alberto Vidal-Diez & Rattana Lerdsuwansri & Chukiat Viwatwongkasem & Mark Arnold, 2013. "A Generalization of Chao's Estimator for Covariate Information," Biometrics, The International Biometric Society, vol. 69(4), pages 1033-1042, December.
    11. Dankmar Böhning, 2010. "Some General Comparative Points on Chao's and Zelterman's Estimators of the Population Size," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 221-236, June.
    12. Chang Xuan Mao & Jun Li, 2009. "Comparing Species Assemblages Via Species Accumulation Curves," Biometrics, The International Biometric Society, vol. 65(4), pages 1063-1067, December.
    13. 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.
    14. 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.
    15. Paul S. F. Yip & Hua-Zhen Lin & Liqun Xi, 2005. "A Semiparametric Method for Estimating Population Size for Capture–Recapture Experiments with Random Covariates in Continuous Time," Biometrics, The International Biometric Society, vol. 61(4), pages 1085-1092, December.
    16. 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.
    17. repec:jss:jstsof:19:i05 is not listed on IDEAS
    18. J. Andrew Royle, 2009. "Analysis of Capture–Recapture Models with Individual Covariates Using Data Augmentation," Biometrics, The International Biometric Society, vol. 65(1), pages 267-274, March.
    19. Zhang, Hongmei & Ghosh, Kaushik & Ghosh, Pulak, 2012. "Sampling designs via a multivariate hypergeometric-Dirichlet process model for a multi-species assemblage with unknown heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2562-2573.
    20. Huggins, Richard, 2007. "On the use of linear models in the estimation of the size of a population using capture-recapture data," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 649-653, March.
    21. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Documents de travail du Centre d'Economie de la Sorbonne 16068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:977-979. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.