Skip to main content
Log in

Reduction problems in comparison of linear models

  • Publications
  • Published:
Metrika Aims and scope Submit manuscript

Abstract

It is shown that comparison of linear models with singular covariance matrices may be reduced to the same problem for non-singular covariance matrices. Moreover the problem of linearly sufficient statistics, considered by Drygas (1983) is reduced to comparison of linear models.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baksalary JK, Kala R (1981) Linear transformations preserving best linear unbiased estimators in a general Gauss-Markoff model. Ann Statist 9:913–916

    MATH  MathSciNet  Google Scholar 

  • Drygas H (1983) Sufficiency and completeness in the general Gauss-Markov model. Sankhyā A 45: 88–98

    MATH  MathSciNet  Google Scholar 

  • Ehrenfeld S (1955) Complete class theorem in experimental design. Proc 3rd Berkeley Symp Math Statist Prob 1:69–75

    Google Scholar 

  • Hansen OH, Torgersen EN (1974) Comparison of linear normal experiments. Ann Statist 2:367–373

    MATH  MathSciNet  Google Scholar 

  • LaMotte LR (1977) A canonical form for general linear model. Ann Statist 5:787–789

    MATH  MathSciNet  Google Scholar 

  • Rao CR (1973) Linear statistical inference and its applications, 2nd ed. Wiley, New York

    MATH  Google Scholar 

  • Stępniak C (1983) Optimal allocation of units in experimental designs with hierarchical and cross classification. Ann Inst Statist Math A 35:461–473

    Article  Google Scholar 

  • Stępniak C (1985) Ordering of nonnegative definite matrices with application to comparison of linear models. Linear Algebra Appl 70:67–71

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  • Stępniak C, Wang SG, Wu CFJ (1984) Comparison of linear experiments with known covariances. Ann Statist 12:35–365

    Google Scholar 

  • Torgersen EN (1976) Comparison of statistical experiments. Scand J Statist 3:186–208

    MathSciNet  Google Scholar 

  • Torgersen E (1984) Orderings of linear models. J Statist Plann and Inference 9:1–17

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stępniak, C. Reduction problems in comparison of linear models. Metrika 34, 211–216 (1987). https://doi.org/10.1007/BF02613151

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02613151

Keywords

Navigation