Insights into the Relationship Between D- and A-optimal Designs

Andrew T. Karl; Bradley Jones

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arXiv · 2603.07252

Insights into the Relationship Between D- and A-optimal Designs

Andrew T. Karl·Bradley Jones

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Abstract

For a fixed linear-model basis, we show that the $A$ criterion factors into an inverse-$D$ scale term and a dimensionless sphericity factor that depends only on eigenvalue dispersion. This factor isolates exactly the part of $A$ not controlled by the determinant, explaining why designs that are exact or near ties in $D$ can differ materially in coefficient-variance, aliasing, and prediction-variance behavior. We illustrate the factorization on a published $D$ tie and on screening settings with infinitely many $D$-optimal solutions, then use the same scale/shape viewpoint as a lightweight post-screen within a space-filling candidate pool. A final section connects the same idea to Kiefer's $\Phi$-class and introduces sphericity profiles.

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Andrew T. Karl, Bradley Jones. 2026-03-07. Insights into the Relationship Between D- and A-optimal Designs. https://arxiv.org/abs/2603.07252

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