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Minimal efficiency of designs under the class of orthogonally invariant information criteria

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  • Radoslav Harman

Abstract

Consider the linear regression model with uncorrelated errors and an experimental design ξ. In the article, we address the problem of calculating the minimal efficiency of ξ with respect to the class [InlineMediaObject not available: see fulltext.] of orthogonally invariant information criteria, containing all Kiefer’s criteria of ϕ p -optimality, among others. We show that the [InlineMediaObject not available: see fulltext.]-minimal efficiency of ξ is equal to the minimal efficiency of ξ with respect to a finite class of criteria which generalize the criterion of E-optimality. We also formulate conditions under which a design is maximin efficient, i.e. the most efficiency-stable for criteria from [InlineMediaObject not available: see fulltext.]. To illustrate the results, we calculated the [InlineMediaObject not available: see fulltext.]-minimal efficiency of ϕ p (in particular D, A and E) optimal designs for polynomial regression on [−1,1] up to degree 4. Moreover, for the quadratic model we explicitly constructed the [InlineMediaObject not available: see fulltext.]-maximin efficient design. Copyright Springer-Verlag 2004

Suggested Citation

  • Radoslav Harman, 2004. "Minimal efficiency of designs under the class of orthogonally invariant information criteria," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(2), pages 137-153, September.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:2:p:137-153
    DOI: 10.1007/s001840300301
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    Cited by:

    1. Katarína Burclová & Andrej Pázman, 2016. "Optimal design of experiments via linear programming," Statistical Papers, Springer, vol. 57(4), pages 893-910, December.
    2. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    3. Samuel Rosa, 2018. "Optimal designs for treatment comparisons represented by graphs," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 479-503, October.
    4. Samuel Rosa & Radoslav Harman, 2016. "Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects," Statistical Papers, Springer, vol. 57(4), pages 1077-1106, December.

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