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Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications

Author

Listed:
  • Song-Nan Liu

    (School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China)

  • Min-Qian Liu

    (School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China)

  • Jin-Yu Yang

    (School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China)

Abstract

For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s 2 × s or s × s 2 grids, and most column pairs satisfy stratifications on s 2 × s 2 grids. Moreover, many column pairs can achieve stratifications on s 4 × s 2 and s 2 × s 4 grids. Furthermore, the obtained space-filling ODs can have s 6 levels, s 4 levels, and mixed levels, as required for different needs.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1549-:d:1104229
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    References listed on IDEAS

    as
    1. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    2. 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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    5. Fasheng Sun & Min-Qian Liu & Dennis K. J. Lin, 2009. "Construction of orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 971-974.
    6. David M. Steinberg & Dennis K. J. Lin, 2006. "A construction method for orthogonal Latin hypercube designs," Biometrika, Biometrika Trust, vol. 93(2), pages 279-288, June.
    7. Fasheng Sun & Boxin Tang, 2017. "A Method of Constructing Space-Filling Orthogonal Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 683-689, April.
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