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Construction of orthogonal general sliced Latin hypercube designs

Author

Listed:
  • Bing Guo

    (Sichuan University)

  • Xiao-Rong Li

    (LPMC & KLMDASR, Nankai University)

  • Min-Qian Liu

    (LPMC & KLMDASR, Nankai University)

  • Xue Yang

    (School of Statistics, Tianjin University of Finance and Economics)

Abstract

Computer experiments have attracted increasing attention in recent decades. General sliced Latin hypercube design (LHD), which is a sliced LHD with multiple layers and at each layer of which each slice can be further divided into smaller LHDs at the above layer, is widely applied in computer experiments with qualitative and quantitative factors, multiple model experiments, cross-validation, and stochastic optimization. Orthogonality is an important property for LHDs. Methods for constructing orthogonal and nearly orthogonal general sliced LHDs are put forward first time in this paper, where orthogonal designs and structural vectors are used in the constructions. The resulting designs not only possess orthogonality in the whole designs, but also achieve orthogonality in each layer before and after being collapsed. Furthermore, based on different structural vectors, the methods can be easily extended to construct orthogonal LHDs with some desired sliced or nested structures.

Suggested Citation

  • Bing Guo & Xiao-Rong Li & Min-Qian Liu & Xue Yang, 2023. "Construction of orthogonal general sliced Latin hypercube designs," Statistical Papers, Springer, vol. 64(3), pages 987-1014, June.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:3:d:10.1007_s00362-022-01347-3
    DOI: 10.1007/s00362-022-01347-3
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    References listed on IDEAS

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    1. Wang, Xiao-Lei & Zhao, Yu-Na & Yang, Jian-Feng & Liu, Min-Qian, 2017. "Construction of (nearly) orthogonal sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 174-180.
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    6. Fasheng Sun & Boxin Tang, 2017. "A general rotation method for orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 104(2), pages 465-472.
    7. Ru Yuan & Bing Guo & Min-Qian Liu, 2021. "Flexible sliced Latin hypercube designs with slices of different sizes," Statistical Papers, Springer, vol. 62(3), pages 1117-1134, June.
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