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On maximin distance and nearly orthogonal Latin hypercube designs

Author

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  • Su, Zheren
  • Wang, Yaping
  • Zhou, Yingchun

Abstract

Maximin distance Latin hypercube designs (LHDs) are frequently used in computer experiments, but their constructions are challenging. In this paper, we present some new results connecting maximin L2-distance optimality and near orthogonality for mirror-symmetric LHDs. We further propose a simple and effective method for constructing nearly orthogonal LHDs that can yield almost the largest minimum distance. The obtained designs with small and medium sizes are tabulated and their superior performances are illustrated via comparisons.

Suggested Citation

  • Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:stapro:v:166:y:2020:i:c:s0167715220301814
    DOI: 10.1016/j.spl.2020.108878
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    References listed on IDEAS

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    1. Ifigenia Efthimiou & Stelios Georgiou & Min-Qian Liu, 2015. "Construction of nearly orthogonal Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 45-57, January.
    2. M. J. Bayarri & James O. Berger & Woncheol Jang & Surajit Ray & Luis R. Pericchi & Ingmar Visser, 2019. "Prior-based Bayesian information criterion," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 3(1), pages 2-13, January.
    3. Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
    4. Qian Xiao & Hongquan Xu, 2017. "Construction of maximin distance Latin squares and related Latin hypercube designs," Biometrika, Biometrika Trust, vol. 104(2), pages 455-464.
    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. Fasheng Sun & Boxin Tang, 2017. "A general rotation method for orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 104(2), pages 465-472.
    7. C. Devon Lin & Rahul Mukerjee & Boxin Tang, 2009. "Construction of orthogonal and nearly orthogonal Latin hypercubes," Biometrika, Biometrika Trust, vol. 96(1), pages 243-247.
    8. Yaping Wang & Jianfeng Yang & Hongquan Xu, 2018. "On the connection between maximin distance designs and orthogonal designs," Biometrika, Biometrika Trust, vol. 105(2), pages 471-477.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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