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Sphere packing design for experiments with mixtures

Author

Listed:
  • Xiong, Zikang
  • Liu, Liwei
  • Ning, Jianhui
  • Qin, Hong

Abstract

Rotated sphere packing design is constructed by scaling, rotating and translating the lattice that has asymptotically lowest fill distance, its space-filling properties are very well. Currently, it can only be used for experimental design in hypercube. In this paper, we generalize the sphere packing design to simplex, which is the domain of experimental design with mixtures. In order to use the lattice method in simplex, a distance preserving transformation function is implemented to transform the simplex into the hyperplane, and then the iteration of rotating, scaling and disturbing is used to extract n lattice points as the design array. Some numerical comparisons between our method and several other popular methods are also provided. The results show that the designs generated by our algorithm are excellent according to the maximin distance criterion and its predictive ability is well. An additional searching method is also suggested to further improve the design.

Suggested Citation

  • Xiong, Zikang & Liu, Liwei & Ning, Jianhui & Qin, Hong, 2020. "Sphere packing design for experiments with mixtures," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301103
    DOI: 10.1016/j.spl.2020.108807
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    References listed on IDEAS

    as
    1. Xu He, 2017. "Rotated Sphere Packing Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1612-1622, October.
    2. Yan Liu & Min-Qian Liu, 2016. "Construction of uniform designs for mixture experiments with complex constraints," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2172-2180, April.
    3. Chuang, S.C. & Hung, Y.C., 2010. "Uniform design over general input domains with applications to target region estimation in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 219-232, January.
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