Skip to main content
SpringerLink
Log in

Homogeneous Linear Estimator and Optimality in Finite Population Sampling

  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

We recall Godambe’s theorem on the nonexistence of an umvue in finite population sampling for estimation of a population total and that the existence of a uniformly minimum mse estimator without any further conditions is not possible. Assuming model-unbiasedness with respect to a well known super population model, we give an alternative derivation of Royall’s optimum estimator. Finally, the role of design unbiasedness criterion is briefly discussed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Basu, D. 1971. An essay on logical foundations of survey sampling. In Foundations of statistical inference, ed V.P. Godambe and D.A. Sprott, 203–233. Toronto, ON: Holt, Rinehart & Winston.

    Google Scholar 

  • Godambe, V. P. 1955. A unified theory of sampling from finite populations. J. R. Stat. Soc. B, 17, 269–278.

    MathSciNet  MATH  Google Scholar 

  • Isaki, C. T., and Fuller, W. A. 1982. Survey design under the regression superpopulation model. J. Am. Stat. Associ., 77, 89–96.

    Article  MathSciNet  Google Scholar 

  • Nayak, T. K. 2003. Finding optimal estimators in survey sampling using unbiased estimators of zero. J. Stat. Plan. Inf., 114, 21–30.

    Article  MathSciNet  Google Scholar 

  • Royall, R. M. 1970. On finite population sampling theory under certain linear regression models. Biometrika, 57, 377–387.

    Article  Google Scholar 

  • Scott, A., and Smith, T. M. F. 1969. Estimation in multi-stage surveys. J. Am. Stat. Assoc., 64, 830–40.

    Article  Google Scholar 

  • Sinha, B. K., and Prasada Rao, P. S. S. N. V. 2011. Godambe’s nonexistence theorem—Revisited and refined through matrix arguments. Technical report, Indian Statistical Institute, Kolkata.

    Google Scholar 

  • Sugden, R. A., and Smith, T. M. F. 2002. Exact linear unbiased estimation in survey sampling, J. Stat. Plan. Inf., 102, 25–38.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. C.R. Rao AIMSCS, University of Hyderabad Campus, Hyderabad, India

    T. J. Rao

Authors
  1. T. J. Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. J. Rao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rao, T.J. Homogeneous Linear Estimator and Optimality in Finite Population Sampling. J Stat Theory Pract 7, 1–7 (2013). https://doi.org/10.1080/15598608.2013.756263

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2013.756263

AMS Subject Classification

Keywords

Search

Navigation