Skip to main content
SpringerLink
Log in

On the A Criterion of Experimental Design

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

Abstract

Consider a linear model with targeted parameters τ. We derive a necessary and sufficient condition on the matrix M for the average variance of functions \(\widehat {{M_\tau}}\) to be proportional to the A value for comparing designs. This establishes the full range of interpretations of the A criterion.

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

  • Atkinson, A. C., A. N. Donev, and R. D. Tobias. 2007. Optimum experimental designs, with SAS. Vol. 34 of Oxford Statistical Science Series. Oxford, UK: Oxford University Press.

    MATH  Google Scholar 

  • Hedayat, A. S., N. J. A. Sloane, and J. Stufken. 1999. Orthogonal arrays. Springer Series in Statistics. New York, NY: Springer-Verlag.

    Book  Google Scholar 

  • Kao, L.-J., P. K. Yates, S. M. Lewis, and A. M. Dean. 1995. Approximate information matrices for estimating a given set of contrasts. Stat. Sinica, 5, 593–598.

    MathSciNet  MATH  Google Scholar 

  • Kempthorne, O. 1956. The efficiency factor of an incomplete block design. Ann. Math. Stat., 27, 846–849.

    Article  MathSciNet  Google Scholar 

  • Kiefer, J. 1958. On the nonrandomized optimality and randomized nonoptimality of symmetrical designs. Ann. Math. Stat., 29, 675–699.

    Article  MathSciNet  Google Scholar 

  • Kiefer, J. 1959. Optimum experimental designs. J. R. Stat. Soc. Ser. B, 21, 272–319.

    MathSciNet  MATH  Google Scholar 

  • Liski, E. P., N. K. Mandal, K. R. Shah, and B. K. Sinha. 2002. Topics in optimal design. Vol. 163 of Lecture Notes in Statistics. New York, NY: Springer-Verlag.

    Book  Google Scholar 

  • Rencher, A. C., and G. B. Schaalje. 2008. Linear models in statistics, 2nd ed. Hoboken, NJ: Wiley-Interscience.

    MATH  Google Scholar 

  • Searle, S. R. 1997. Linear models. Wiley Classics Library. New York, NY: John Wiley & Sons. (Originally published 1971.)

    Book  Google Scholar 

  • Shah, K. R., and B. K. Sinha. 1989. Theory of optimal designs. Vol. 54 of Lecture Notes in Statistics. New York, NY: Springer-Verlag.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Virginia Tech, Blacksburg, Virginia, 24061-0439, USA

    J. P. Morgan & J. W. Stallings

Authors
  1. J. P. Morgan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. W. Stallings
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. P. Morgan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Morgan, J.P., Stallings, J.W. On the A Criterion of Experimental Design. J Stat Theory Pract 8, 418–422 (2014). https://doi.org/10.1080/15598608.2013.769922

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1080/15598608.2013.769922

Keywords

Search

Navigation