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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07252 |
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| _version_ | 1866908877492060160 |
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| author | Karl, Andrew T. Jones, Bradley |
| author_facet | Karl, Andrew T. Jones, Bradley |
| contents | 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 $Φ$-class and introduces sphericity profiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Insights into the Relationship Between D- and A-optimal Designs Karl, Andrew T. Jones, Bradley Methodology 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 $Φ$-class and introduces sphericity profiles. |
| title | Insights into the Relationship Between D- and A-optimal Designs |
| topic | Methodology |
| url | https://arxiv.org/abs/2603.07252 |