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Focused Information Criterion for Capture–Recapture Models for Closed Populations

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  • FRANCESCO BARTOLUCCI
  • MONIA LUPPARELLI

Abstract

. We propose a criterion for selecting a capture–recapture model for closed populations, which follows the basic idea of the focused information criterion (FIC) of Claeskens and Hjort. The proposed criterion aims at selecting the model which, among the available models, leads to the smallest mean‐squared error (MSE) of the resulting estimator of the population size and is based on an index which, up to a constant term, is equal to the asymptotic MSE of the estimator. Two alternative approaches to estimate this FIC index are proposed. We also deal with multimodel inference; in this case, the population size is estimated by using a weighted average of the estimates coming from different models, with weights chosen so as to minimize the MSE of the resulting estimator. The proposed model selection approach is compared with more common approaches through a series of simulations. It is also illustrated by an application based on a dataset coming from a live‐trapping experiment.

Suggested Citation

  • Francesco Bartolucci & Monia Lupparelli, 2008. "Focused Information Criterion for Capture–Recapture Models for Closed Populations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 629-649, December.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:4:p:629-649
    DOI: 10.1111/j.1467-9469.2008.00604.x
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    References listed on IDEAS

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    1. S. E. Fienberg & M. S. Johnson & B. W. Junker, 1999. "Classical multilevel and Bayesian approaches to population size estimation using multiple lists," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 383-405.
    2. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
    3. Bartolucci, Francesco & Forcina, Antonio, 2006. "A Class of Latent Marginal Models for CaptureRecapture Data With Continuous Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 786-794, June.
    4. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
    5. Shirley Pledger, 2000. "Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures," Biometrics, The International Biometric Society, vol. 56(2), pages 434-442, June.
    6. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
    7. Claeskens G. & Hjort N.L., 2003. "The Focused Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 900-916, January.
    8. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    Cited by:

    1. Gerda Claeskens, 2012. "Focused estimation and model averaging with penalization methods: an overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(3), pages 272-287, August.
    2. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.

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