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A correction to make Chao estimator conservative when the number of sampling occasions is finite

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  • Farcomeni, Alessio
  • Dotto, Francesco

Abstract

Chao estimator is not guaranteed to be asymptotically conservative with finite sampling efforts. A simple correction solves the issue. We illustrate with simulations and examples that the corrected Chao estimator is asymptotically conservative, and has lower standard error.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:176:y:2021:i:c:s0167715221001164
    DOI: 10.1016/j.spl.2021.109154
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    References listed on IDEAS

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    1. Pedro Puig & Célestin C. Kokonendji, 2018. "Non†parametric Estimation of the Number of Zeros in Truncated Count Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 347-365, June.
    2. Anne Chao & Chih-Wei Lin, 2012. "Nonparametric Lower Bounds for Species Richness and Shared Species Richness under Sampling without Replacement," Biometrics, The International Biometric Society, vol. 68(3), pages 912-921, September.
    3. Lanumteang, K. & Böhning, D., 2011. "An extension of Chao's estimator of population size based on the first three capture frequency counts," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2302-2311, July.
    4. Chun-Huo Chiu & Yi-Ting Wang & Bruno A. Walther & Anne Chao, 2014. "An improved nonparametric lower bound of species richness via a modified good–turing frequency formula," Biometrics, The International Biometric Society, vol. 70(3), pages 671-682, September.
    5. A. Farcomeni, 2016. "A general class of recapture models based on the conditional capture probabilities," Biometrics, The International Biometric Society, vol. 72(1), pages 116-124, March.
    6. 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.
    7. Mao, Chang Xuan, 2006. "Inference on the Number of Species Through Geometric Lower Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1663-1670, December.
    8. Louis-Paul Rivest & Sophie Baillargeon, 2007. "Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population," Biometrics, The International Biometric Society, vol. 63(4), pages 999-1006, December.
    9. Baillargeon, Sophie & Rivest, Louis-Paul, 2007. "Rcapture: Loglinear Models for Capture-Recapture in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i05).
    Full references (including those not matched with items on IDEAS)

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