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Environmental and Ecological Statistics

, Volume 18, Issue 3, pp 543–568 | Cite as

Leveraging the Rao–Blackwell theorem to improve ratio estimators in adaptive cluster sampling

  • Chang-Tai Chao
  • Arthur L. Dryver
  • Tzu-Ching Chiang
Article

Abstract

Rao-Blackwellization is used to improve the unbiased Hansen–Hurwitz and Horvitz–Thompson unbiased estimators in Adaptive Cluster Sampling by finding the conditional expected value of the original unbiased estimators given the sufficient or minimal sufficient statistic. In principle, the same idea can be used to find better ratio estimators, however, the calculation of taking all the possible combinations into account can be extremely tedious in practice. The simplified analytical forms of such ratio estimators are not currently available. For practical interest, several improved ratio estimators in Adaptive Cluster Sampling are proposed in this article. The proposed ratio estimators are not the real Rao-Blackwellized versions of the original ones but make use of the Rao-Blackwellized univariate estimators. How to calculate the proposed estimators is illustrated, and their performance are evaluated by both of the Bivariate Poisson clustered process and a real data. The simulation result indicates that the proposed improved ratio estimators are able to provide considerably advantageous estimation results over the original ones.

Keywords

Adaptive cluster sampling Ratio estimator Rao-Blackwellization Sufficient statistic Minimal sufficient statistic Hansen–Hurwitz estimation Horvitz–Thompson estimation 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Chang-Tai Chao
    • 1
  • Arthur L. Dryver
    • 2
  • Tzu-Ching Chiang
    • 1
  1. 1.Department of Statistics, School of ManagementNational Cheng-Kung UniversityTainanTaiwan
  2. 2.Graduate School of Business AdministrationNational Institute of Development AdministrationBangkokThailand

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