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Environmental and Ecological Statistics

, Volume 17, Issue 1, pp 111–123 | Cite as

Empirical likelihood confidence intervals for adaptive cluster sampling

  • Mohammad Salehi
  • Mohammad Mohammadi
  • J. N. K. Rao
  • Yves G. Berger
Article

Abstract

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.

Keywords

Finite population Hansen-Hurwitz estimator Horvitz-Thompson estimator Empirical likelihood ratio 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Mohammad Salehi
    • 1
    • 2
  • Mohammad Mohammadi
    • 1
  • J. N. K. Rao
    • 3
  • Yves G. Berger
    • 4
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.Statistical Research and Training Center (SRTC)TehranIran
  3. 3.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  4. 4.Southampton Statistical Sciences Research InstituteUniversity of SouthamptonSouthamptonUK

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