Skip to main content
SpringerLink
Log in

Bayes equivariant estimators in a crossed classification random effects model

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

The Bayes equivariant estimators of the variance components in the two-way crossed classification random effects model withK (K=>1) observations per cell are characterized under the usual assumptions of normality and independence of the random effects. An illustrative example of non-trivial Bayes equivariant estimators derived using a special prior distribution is provided. It is pointed out that for the squared error loss function every Bayes equivariant estimator of the residual variance component is inadmissible.

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

  1. Box, G. E. P. and Tiao, G. C. (1973).Bayesian Inference in Statistical Analysis, Addision Wesley Publishing Co., Reading Massachusetts.

    MATH  Google Scholar 

  2. Klotz, J. H., Milton, R.C. and Zacks, S. (1969). Mean square efficiency of estimators of variance components,J. Amer. Statist Ass.,64, 1383–1402.

    Article  MathSciNet  MATH  Google Scholar 

  3. Lehmann, E. L. and Scheffé, H. (1950). Completeness, similar regions and unbiased estimation, Part I,Sankhyä,10, 305–340.

    MATH  Google Scholar 

  4. Sahai, H. (1975). Bayes, equivarian estimators in high order hierarchical random effects models,J. Roy. Statist. Soc., Ser. B,37, 193–197.

    MathSciNet  MATH  Google Scholar 

  5. Sahai, H. (1975). A comparison of estimators of variance components in the two-way crossed classification random effects model using mean squared error criterion, submitted.

  6. Sahai, H. and Ramirez-Martines (1975). Some formal Bayes estimators of variance components in a crossed classification random effects model.Aust. J. Statist (in press).

  7. Stein, C. (1964). Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean,Ann. Inst. Statist Math.,16, 155–160.

    Article  MathSciNet  Google Scholar 

  8. Tiao, G. C. and Guttman, I. (1965). The inverted Dirichlet distribution with applications.J. Amer. Statist. Ass.,60, 793–805.

    Article  MATH  Google Scholar 

  9. Zacks, S. (1970). Bayes equivariant estimators of variance components,Ann. Inst. Statist. Math.,22, 27–40.

    Article  MathSciNet  MATH  Google Scholar 

  10. Zacks, S. (1971).The Theory of Statistical Inference, John Wiley & Sons, Inc., New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Puerto Rico, Puerto Rico

    Hardeo Sahai

Authors
  1. Hardeo Sahai
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Sahai, H. Bayes equivariant estimators in a crossed classification random effects model. Ann Inst Stat Math 27, 501–505 (1975). https://doi.org/10.1007/BF02504667

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02504667

Keywords

Search

Navigation