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Strong orthogonal arrays and associated Latin hypercubes for computer experiments

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  • Yuanzhen He
  • Boxin Tang

Abstract

This paper introduces, constructs and studies a new class of arrays, called strong orthogonal arrays, as suitable designs for computer experiments. A strong orthogonal array of strength t enjoys better space-filling properties than a comparable orthogonal array in all dimensions lower than t while retaining the space-filling properties of the latter in t dimensions. Latin hypercubes based on strong orthogonal arrays of strength t are more space-filling than comparable orthogonal array-based Latin hypercubes in all g dimensions for any 2 ≤ g ≤ t - 1. Copyright 2013, Oxford University Press.

Suggested Citation

  • Yuanzhen He & Boxin Tang, 2013. "Strong orthogonal arrays and associated Latin hypercubes for computer experiments," Biometrika, Biometrika Trust, vol. 100(1), pages 254-260.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:1:p:254-260
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    File URL: http://hdl.handle.net/10.1093/biomet/ass065
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    Cited by:

    1. Song-Nan Liu & Min-Qian Liu & Jin-Yu Yang, 2023. "Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    2. Zujun Ou & Minghui Zhang & Hongyi Li, 2023. "Triple Designs: A Closer Look from Indicator Function," Mathematics, MDPI, vol. 11(3), pages 1-12, February.
    3. 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.
    4. Yuxin Sun & Wenjun Liu & Ye Tian, 2024. "Projection-Uniform Subsampling Methods for Big Data," Mathematics, MDPI, vol. 12(19), pages 1-16, September.
    5. Wang, Chunyan & Lin, Dennis K.J., 2024. "Strong orthogonal Latin hypercubes for computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 198(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. Grömping, Ulrike, 2023. "A unifying implementation of stratum (aka strong) orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    8. 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).
    9. Li, Hui & Yang, Liuqing & Liu, Min-Qian, 2022. "Construction of space-filling orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 180(C).

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