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A unifying implementation of stratum (aka strong) orthogonal arrays

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  • Grömping, Ulrike

Abstract

Constructions of so-called “strong orthogonal arrays” (SOAs) have been previously proposed. The approaches and notations taken in the different proposals vary widely. The SOAs and their constructions are reviewed using a unifying notation with a simple set of equations. In addition to providing a unifying overview, some constructions are improved, e.g., by enforcing column orthogonality via a bipartite pair matching algorithm where the original constructions pay no attention to column orthogonality. All presented constructions are implemented in the R package SOAs. As an aside, it is argued that “stratum” is a better choice than “strong” for the “S” in the acronym SOAs.

Suggested Citation

  • Grömping, Ulrike, 2023. "A unifying implementation of stratum (aka strong) orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:csdana:v:183:y:2023:i:c:s0167947323000506
    DOI: 10.1016/j.csda.2023.107739
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    References listed on IDEAS

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    1. Yongdao Zhou & Boxin Tang, 2019. "Column-orthogonal strong orthogonal arrays of strength two plus and three minus," Biometrika, Biometrika Trust, vol. 106(4), pages 997-1004.
    2. Wenlong Li & Min-Qian Liu & Jian-Feng Yang, 2022. "Construction of column-orthogonal strong orthogonal arrays," Statistical Papers, Springer, vol. 63(2), pages 515-530, April.
    3. Ye Tian & Hongquan Xu, 2022. "A minimum aberration-type criterion for selecting space-filling designs [Optimal sliced Latin hypercube designs]," Biometrika, Biometrika Trust, vol. 109(2), pages 489-501.
    4. Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    5. Jiang, Bochuan & Wang, Zuzheng & Wang, Yaping, 2021. "Strong orthogonal arrays of strength two-plus based on the Addelman–Kempthorne method," Statistics & Probability Letters, Elsevier, vol. 175(C).
    6. Mengmeng Liu & Min-Qian Liu & Jinyu Yang, 2022. "Construction of group strong orthogonal arrays of strength two plus," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 657-674, August.
    7. Derek Bingham & Randy R. Sitter & Boxin Tang, 2009. "Orthogonal and nearly orthogonal designs for computer experiments," Biometrika, Biometrika Trust, vol. 96(1), pages 51-65.
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