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Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random

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  • Yang Liu
  • Yukun Liu
  • Pengfei Li
  • Lin Zhu

Abstract

In capture‐recapture experiments, individual covariates may be subject to missingness, especially when the number of captures is small. When the covariate information is missing at random, the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance. These estimators are then used to construct Wald‐type confidence intervals. However, such intervals may have seriously inaccurate coverage probabilities. In this paper, we propose a maximum empirical likelihood (EL) estimation approach for the abundance in the presence of missing covariates. We show that the maximum EL estimator is asymptotically normal, and that the EL ratio statistic for the abundance has a chi‐square limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has a smaller mean square error than existing estimators, and the proposed EL ratio confidence interval usually has more accurate coverage probabilities than the existing Wald‐type confidence intervals. We illustrate the proposed method by analyzing data collected in Hong Kong for the yellow‐bellied prinia, a bird species.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:1050-1060
    DOI: 10.1111/biom.13334
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Richard Huggins & Wen‐Han Hwang, 2011. "A Review of the Use of Conditional Likelihood in Capture‐Recapture Experiments," International Statistical Review, International Statistical Institute, vol. 79(3), pages 385-400, December.
    4. Shen‐Ming Lee & Wen‐Han Hwang & Jean de Dieu Tapsoba, 2016. "Estimation in closed capture–recapture models when covariates are missing at random," Biometrics, The International Biometric Society, vol. 72(4), pages 1294-1304, December.
    5. Yang Liu & Yukun Liu & Pengfei Li & Jing Qin, 2018. "Full likelihood inference for abundance from continuous time capture–recapture data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 995-1014, November.
    6. 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.
    7. Yan Wang & Paul S. F. Yip, 2003. "A Semiparametric Model for Recapture Experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 667-676, December.
    8. Paul S. F. Yip & Yan Wang, 2002. "A Unified Parametric Regression Model for Recapture Studies with Random Removals in Continuous Time," Biometrics, The International Biometric Society, vol. 58(1), pages 192-199, March.
    9. Wen-Han Hwang & Steve Y. H. Huang, 2003. "Estimation in Capture-Recapture Models When Covariates Are Subject to Measurement Errors," Biometrics, The International Biometric Society, vol. 59(4), pages 1113-1122, December.
    10. D. Y. Lin & P. S. F. Yip, 1999. "Parametric regression models for continuous time removal and recapture studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 401-411, April.
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