Skip to main content
SpringerLink
Log in

Rao-Blackwell Modifications

  • Chapter
  • First Online:
Book cover Adaptive Sampling Designs

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

  • 1864 Accesses

Abstract

This chapter summarizes some foundational theory for adaptive sampling methods. The Rao-Blackwell theorem can be applied to unbiased estimators to provide more efficient estimators. Closed form expressions for these and related estimators are discussed. The theory is also applied to selecting networks without replacement, and the question of ignoring information from labels is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    These concepts are more difficult for a finite population.

References

  • Chao C-T., A.L. Dryver, and T.C. Chiang. 2011. “Leveraging the Rao-Blackwell Theorem to Improve Ratio Estimators in Adaptive Cluster sampling.” Environmental and Ecological Statistics DOI:10.1007/s10651-010-0151-y.

  • Dryver, A.L., and C-T. Chao. 2007. “Ratio Estimators in Adaptive Cluster Sampling.” Environmetrics 18:607–620.

    Google Scholar 

  • Dryver, A.L., and S.K. Thompson. 2005. “Improved Unbiased Estimators in Adaptive Cluster Sampling.” Journal of the Royal Statistical Society 67(1):157–166.

    Google Scholar 

  • Félix-Medina, M.H. 2000. “Analytical Expressions for Rao-Blackwell Estimators in Adaptive Cluster Sampling.” Journal of Statistical Planning and Inference 84:221–236.

    Google Scholar 

  • Low K.H., G.J. Gordon, J.M. Dolan, and P. Khosla. 2005. “Adaptive Sampling for Multi-Robot Wide Area Prospecting.” Robotics Institute, CMU, Pittsburgh, PA, Tech. Rep. CMU-RI-TR-05-51. (See http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.72.4649.)

  • Salehi M.M. 1999. “Rao-Blackwell Versions of the Horvitz-Thompson and Hansen-Hurwitz Estimators in Adaptive Cluster Sampling.” Journal of Environmental and Ecological Statistics 6:183–195.

    Google Scholar 

  • Salehi M.M. 2001. “Application of Adaptive Sampling in Fishery, Part 1: Adaptive Cluster Sampling and Its Strip Versions.” Iranian Journal of Fisheries Sciences 3(1):55–76.

    Google Scholar 

  • Salehi M. M. 2003. “Comparison Between Hansen-Hurwitz and Horvitz- Estimators for Adaptive Cluster Sampling.” Journal of Environmental and Ecological Statistics 10(1):115–127.

    Google Scholar 

  • Salehi M. M., and G.A.F. Seber. 1997. “Adaptive Cluster Sampling Design with the Networks Selected without Replacement.” Biometrika 84:209–219.

    Google Scholar 

  • Smith, D. R., M.J. Conroy, and D.H. Brakhage. 1995. “Efficiency of Adaptive Cluster Sampling for Estimating Density of Wintering Waterfowl.” Biometrics 51:777–788.

    Google Scholar 

  • Thompson, S.K., and G.A.F. Seber. 1996. Adaptive Sampling. New York: Wiley.

    Google Scholar 

  • Turk, P., and J.J. Borkowski. 2005. “A Review of Adaptive Cluster Sampling: 1990–2003.” Environmental and Ecological Statistics 12:55–94.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1.  , 7 Milford Park Place, 0620, North Shore, New Zealand

    George A. F. Seber

  2. Department of Statistics, University of Auckland, Auckland, New Zealand

    George A. F. Seber

  3. Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

    Mohammad M. Salehi

Authors
  1. George A. F. Seber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad M. Salehi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George A. F. Seber .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 The Author(s)

About this chapter

Cite this chapter

Seber, G.A.F., Salehi, M.M. (2012). Rao-Blackwell Modifications. In: Adaptive Sampling Designs. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33657-7_3

Download citation

Publish with us

Policies and ethics

Search

Navigation