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Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture data

Author

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  • Yukun Liu
  • Pengfei Li
  • Jing Qin

Abstract

SummaryCapture-recapture experiments are widely used to collect data needed for estimating the abundance of a closed population. To account for heterogeneity in the capture probabilities, Huggins (1989) and Alho (1990) proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified. A conditional likelihood method was then proposed to obtain point estimates and Wald-type confidence intervals for the abundance. Empirical studies show that the small-sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right, which may produce Wald-type confidence intervals with lower limits that are less than the number of captured individuals or even are negative. In this paper, we propose a full empirical likelihood approach based on Huggins and Alho’s model. We show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi-squared with one degree of freedom, and that the maximum empirical likelihood estimator achieves semiparametric efficiency. Simulation studies show that the empirical likelihood-based method is superior to the conditional likelihood-based method: its confidence interval has much better coverage, and the maximum empirical likelihood estimator has a smaller mean square error. We analyse three datasets to illustrate the advantages of our empirical likelihood approach.

Suggested Citation

  • Yukun Liu & Pengfei Li & Jing Qin, 2017. "Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture data," Biometrika, Biometrika Trust, vol. 104(3), pages 527-543.
  • Handle: RePEc:oup:biomet:v:104:y:2017:i:3:p:527-543.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx038
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    Citations

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    Cited by:

    1. Yang Liu & Yukun Liu & Yan Fan & Han Geng, 2018. "Likelihood ratio confidence interval for the abundance under binomial detectability models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 549-568, July.
    2. Mengke Li & Yukun Liu & Pengfei Li & Jing Qin, 2022. "Empirical likelihood meta-analysis with publication bias correction under Copas-like selection model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 93-112, February.
    3. Yulu Ji & Yang Liu, 2024. "A Penalized Empirical Likelihood Approach for Estimating Population Sizes under the Negative Binomial Regression Model," Mathematics, MDPI, vol. 12(17), pages 1-23, August.
    4. Yang Liu & Yukun Liu & Pengfei Li & Lin Zhu, 2021. "Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random," Biometrics, The International Biometric Society, vol. 77(3), pages 1050-1060, September.
    5. Wen-Han Hwang & Jakub Stoklosa & Ching-Yun Wang, 2022. "Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 303-320, June.

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