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Theory and applications of stratification criteria based on space-filling pattern and projection pattern

Author

Listed:
  • Xinqi Zhang

    (Northeast Normal University
    Hulunbuir University)

  • Yaping Wang

    (East China Normal University)

  • Fasheng Sun

    (Northeast Normal University)

Abstract

Space-filling designs are crucial for computer experiments. The quality of a space-filling design can be appropriately reflected by its stratification properties. In a recent paper, Tian and Xu (Biometrika 109(2):489–501, 2022) introduced the concept of a space-filling pattern to properly characterize a design’s stratification properties on various grids. In this study, we generalize the space-filling pattern using arbitrary orthonormal contrasts. We also propose a new pattern called the two-dimensional projection pattern to capture the stratification properties of balanced designs in two dimensions more comprehensively. We derive some theoretical results for both patterns and show that they are easier to compute and apply to a wider range of designs. We further show the use of the two patterns in constructing space-filling designs based on existing strong orthogonal arrays.

Suggested Citation

  • Xinqi Zhang & Yaping Wang & Fasheng Sun, 2025. "Theory and applications of stratification criteria based on space-filling pattern and projection pattern," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(4), pages 445-468, May.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:4:d:10.1007_s00184-024-00964-2
    DOI: 10.1007/s00184-024-00964-2
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    References listed on IDEAS

    as
    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. 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.
    3. Yaping Wang & Fasheng Sun & Hongquan Xu, 2022. "On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 375-385, January.
    Full references (including those not matched with items on IDEAS)

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