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

Radoslav Harman ()

Metrika: International Journal for Theoretical and Applied Statistics, 2004, vol. 60, issue 2, 137-153

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

Keywords: Optimal design; Efficiency of designs; E-optimality; Maximin design; Polynomial regression (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:60:y:2004:i:2:p:137-153

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DOI: 10.1007/s001840300301

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