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Uniform projection nested Latin hypercube designs

Author

Listed:
  • Hao Chen

    (Tianjin University of Finance and Economics)

  • Yan Zhang

    (Tianjin University of Finance and Economics Pearl River College)

  • Xue Yang

    (Tianjin University of Finance and Economics)

Abstract

Computer experiments usually involve many factors, but only a few of them are active. In such a case, it is desirable to construct designs with good projection properties. Maximum projection designs and uniform projection designs have been developed for common experimental situations, however, there has been little study on constructing projection designs for high-accuracy computer experiments (HEs) and low-accuracy computer experiments (LEs) so far. In this paper, we propose a weighted uniform projection criterion, and construct uniform projection nested Latin hypercube designs to suit such computer experiment situations. We show that the obtained designs have good projection properties in all sub-dimensions, and we also discuss how to choose a proper value for the weight. Simulated examples are available to illustrate the effectiveness of the proposed designs.

Suggested Citation

  • Hao Chen & Yan Zhang & Xue Yang, 2021. "Uniform projection nested Latin hypercube designs," Statistical Papers, Springer, vol. 62(4), pages 2031-2045, August.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:4:d:10.1007_s00362-020-01172-6
    DOI: 10.1007/s00362-020-01172-6
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    References listed on IDEAS

    as
    1. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
    2. Peter Z. G. Qian, 2009. "Nested Latin hypercube designs," Biometrika, Biometrika Trust, vol. 96(4), pages 957-970.
    3. van Dam, E.R. & Husslage, B.G.M. & den Hertog, D., 2004. "One-Dimensional Nested Maximin Designs," Other publications TiSEM f2db4179-7b8e-4b7c-a736-7, Tilburg University, School of Economics and Management.
    4. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    5. Hao Chen & Min-Qian Liu, 2015. "Nested Latin Hypercube Designs with Sliced Structures," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(22), pages 4721-4733, November.
    6. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    7. Xu, Jin & Duan, Xiaojun & Wang, Zhengming & Yan, Liang, 2018. "A general construction for nested Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 134-140.
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