Skip to main content
SpringerLink
Log in

Order relations for linear models: A survey on recent developments

  • Survey Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Summary

In this survey the most applicable order relations between linear experiments are studied. For linear normal experiments the cases of known and unknown variances require sophisticated arguments from linear algebra and some tools from convexity theory. The comparison of linear experiments also casts some new light on the popular statistical notions of sufficiency and deficiency.

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. S. Ehrenfeld: Complete class theorem in experimental design Proc. 3rd Berkeley Symp. on Math. Statist. Probab. Vol. 1 (1955), 57–67

    Google Scholar 

  2. O. H. Hansen, E. N. Torgersen: Comparison of linear normal experiments Ann. Statist. 2 (1974), 367–373

    MATH  MathSciNet  Google Scholar 

  3. H. Heyer: Theory of Statistical Experiments Springer, New York-Heidelberg-Berlin 1982

    MATH  Google Scholar 

  4. J. Kiefer: Optimum experimental designs J. Roy. Statist. Soc. Ser. B, 21 (1959), 272–319.

    MATH  MathSciNet  Google Scholar 

  5. L. LeCam: Asymptotic Methods in Statistical Decision Theory Springer New York-Heidelberg-Berlin-London-Paris-Tokyo 1986

    Google Scholar 

  6. E. L. Lehmann: Comparison of experiments for some multivariate normal situations In: Studies in economic time series and multivariate statistics (edited by S. Karlin, T. Arnemiya, L. A. Goodman), pp. 491–503 Academic Press, New York-London 1983

    Google Scholar 

  7. E. L. Lehmann: Comparing location experiments Ann. Statist. 16 (1988), 521–533

    MATH  MathSciNet  Google Scholar 

  8. C. R. Rao: Linear Statistical Inference and Its Applications 2nd ed. Wiley, New York 1973

    MATH  Google Scholar 

  9. C. Stępniak: Ordering of nonnegative definite matrices with application to comparison of linear models Linear Algebra and its Applications 70 (1985), 67–71

    Article  MathSciNet  Google Scholar 

  10. C. Stępniak: Comparing normal linear experiments and white noise Unpublished 1997

  11. C. Stępniak: Comparison of normal linear experiments by quadratic forms Ann. Inst. Statist. Math. Vol. 49, No 3 (1997), 569–584

    Article  MathSciNet  Google Scholar 

  12. C. Stępniak: Matrix loss in comparison of linear experiments Linear Algebra Appl. 264 (1997), 341–348

    Article  MathSciNet  Google Scholar 

  13. C. Stępniak: Comparing normal linear experiments and transformation of observations Statitics 30 (1998), 279–289

    Google Scholar 

  14. C. Stępniak: On comparing experiments and transformation of observations unpublished 1999

  15. C. Stępniak: On matrix results in comparison of linear experiments Linear Algebra and its Applications 321 (2000), 321–325

    Article  MathSciNet  Google Scholar 

  16. C. Stępniak, E. Torgersen: Comparison of linear models with partially known covariances with respect to unbiased estimation Scand. J. Statistics 8 (1981), 183–184

    Google Scholar 

  17. C. Stępniak, S.-G. Wang, C. F. J. Wu: Comparison of linear experiments with known covariances Ann. Statist. 12 (1984), 358–365

    MathSciNet  Google Scholar 

  18. H. Strasser: Mathematical Theory of Statistics De Gruyter, Berlin-New York 1985

    MATH  Google Scholar 

  19. K. Takeuchi: On optimal design (in Japanese) Keiei Kagaku (1961), 23–39

  20. E. Torgersen: Ordering of linear models J. Statist. Plann. Inference 9 (1984), 1–17

    Article  MATH  MathSciNet  Google Scholar 

  21. E. Torgersen: Comparison of Statistical Experiments Cambridge Univ. Press 1991

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität, Auf der Morgenstelle 10 Block C, 72076, Tübingen

    Herbert Heyer

Authors
  1. Herbert Heyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heyer, H. Order relations for linear models: A survey on recent developments. Statistical Papers 47, 331–372 (2006). https://doi.org/10.1007/s00362-006-0293-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-006-0293-z

Keywords

Search

Navigation