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Exact optimality of augmented order-of-addition designs — arXiv:2611.08793

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.08793
License (as archived): CC0-1.0
Archived: 2026-11-09T22:42:41.611Z
SHA-256 of the archived text: 0dc6cbfd4b02991e670ea03259629dd5433fd0e9fdfeb9b1aa77aeec882eaf9f
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How to cite

Exact optimality of augmented order-of-addition designs — arXiv:2611.08793 — arXiv (en), https://arxiv.org/abs/2611.08793 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_32033ecfcd6f (Metraipolis archive dc_32033ecfcd6f, sha256 0dc6cbfd4b02991e670ea03259629dd5433fd0e9fdfeb9b1aa77aeec882eaf9f)

BibTeX

@misc{dc32033ecfcd6f,
  title = {Exact optimality of augmented order-of-addition designs — arXiv:2611.08793},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.08793},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_32033ecfcd6f; sha256 0dc6cbfd4b02991e670ea03259629dd5433fd0e9fdfeb9b1aa77aeec882eaf9f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.08793. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove that, for the pairwise-ordering model with at least three components, adding any run to an order-of-addition orthogonal array gives a $D$-optimal design among all exact designs of the enlarged size, allowing replication. We also establish the corresponding result for foldover designs: adding any reversal pair to a foldover order-of-addition orthogonal array gives a $D$-optimal design within the foldover class at the enlarged size. Both augmentations also minimise the average prediction variance and a covariance-scaled information discrepancy, and maximise the minimum relative efficiency. The key step represents the scaled discrepancy through signed comparisons of triples and derives a sharp integer lower bound; classical spectral inequalities then give the exact-size optima, and signed four-component relative-order counts characterise equality. Complete reversal pairs additionally protect the estimation of pairwise-ordering effects against arbitrary reversal-invariant nuisance means. At the smallest estimable five-component foldover size, exact enumeration identifies five determinant-optimal classes with different prediction and balance properties, and a seven-component example shows that deleting a reversal pair need not be optimal even when it minimises the discrepancy. Constructions through ten components illustrate the attained run sizes.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.ST, nuovi lavori del giorno).
Categorie arXiv: Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2611.08793 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-09T22:35:47.235Z dalla pagina https://arxiv.org/list/math.ST/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).