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Metrika

, Volume 81, Issue 5, pp 549–568 | Cite as

Likelihood ratio confidence interval for the abundance under binomial detectability models

  • Yang Liu
  • Yukun Liu
  • Yan Fan
  • Han Geng
Article
  • 104 Downloads

Abstract

Binomial detectability models are often used to estimate the size or abundance of a finite population in biology, epidemiology, demography and reliability. Special cases include incompletely observed multinomial models, capture–recapture models, and distance sampling models. The most commonly-used confidence interval for the abundance is the Wald-type confidence interval, which is based on the asymptotic normality of a reasonable point estimator of the abundance. However, the Wald-type confidence interval may have poor coverage accuracy and its lower limit may be less than the number of observations. In this paper, we rigorously establish that the likelihood ratio test statistic for the abundance under the binomial detectability models follows the chisquare limiting distribution with one degree of freedom. This provides a solid theoretical justification for the use of the proposed likelihood ratio confidence interval. Our simulations indicate that in comparison to the Wald-type confidence interval, the likelihood ratio confidence interval not only has more accurate coverage rate, but also exhibits more stable performance in a variety of binomial detectability models. The proposed interval is further illustrated through analyzing three real data-sets.

Keywords

Abundance Binomial detectability models Capture-recapture models Confidence interval Distance sampling models 

Notes

Acknowledgements

We are grateful to the editor and two anonymous referees for their insightful and constructive comments which led to an improved presentation of this article. The research was supported by National Natural Science Foundation of China (Grant Nos. 11501354, 11771144, 11371142, and 11501208), Program of Shanghai Subject Chief Scientist (14XD1401600) and the 111 Project (B14019).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of StatisticsEast China Normal UniversityShanghaiChina
  2. 2.School of Statistics and InformationShanghai University of International Business and EconomicsShanghaiChina

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