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 of orthogonally invariant information criteria, containing all Kiefer’s criteria of ϕ p -optimality, among others. We show that the -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 . To illustrate the results, we calculated the -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 -maximin efficient design.
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Acknowledgement. The author would like to thank prof. Pázman as well as an anonymous referee for useful and inspiring comments on earlier versions of this article.
Supported by: VEGA grant of the Slovak Agency No. 1/0264/03
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Harman, R. Minimal efficiency of designs under the class of orthogonally invariant information criteria. Metrika 60, 137–153 (2004). https://doi.org/10.1007/s001840300301
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DOI: https://doi.org/10.1007/s001840300301