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Fully general Chao and Zelterman estimators with application to a whale shark population

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  • Alessio Farcomeni

Abstract

We introduce generalized Chao and generalized Zelterman estimators which include individual, time varying and behavioural effects. Under mild assumptions in the presence of unobserved heterogeneity, the generalized Chao estimator asymptotically provides a lower bound for the population size and is unbiased otherwise. Corrected versions guarantee bounded estimates. To include the best set of predictors we propose the biased empirical focused information criterion bFIC. Simulations indicate that bFIC might give considerable improvements over other selection criteria in our context. We illustrate with an original application to size estimation of a whale shark (Rhincodon typus) population in South Ari Atoll, in the Maldives.

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  • Alessio Farcomeni, 2018. "Fully general Chao and Zelterman estimators with application to a whale shark population," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(1), pages 217-229, January.
    • Handle: RePEc:bla:jorssc:v:67:y:2018:i:1:p:217-229
    DOI: 10.1111/rssc.12219
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    Cited by:

    1. Farcomeni, Alessio & Dotto, Francesco, 2021. "A correction to make Chao estimator conservative when the number of sampling occasions is finite," Statistics & Probability Letters, Elsevier, vol. 176(C).
    2. Linda Altieri & Alessio Farcomeni & Danilo Alunni Fegatelli, 2023. "Continuous time‐interaction processes for population size estimation, with an application to drug dealing in Italy," Biometrics, The International Biometric Society, vol. 79(2), pages 1254-1267, June.

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