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Construction of uniform mixed-level designs through level permutations

Author

Listed:
  • Bochuan Jiang

    (Beijing Jiaotong University)

  • Fei Wang

    (Peking University)

  • Yaping Wang

    (East China Normal University)

Abstract

Uniform designs have been widely used in physical and computer experiments due to their robust performances. The level permutation method can efficiently construct uniform designs with both lower discrepancy and less aberration. However, the related existing literature has mostly discussed uniform fixed-level designs, the construction of uniform mixed-level designs has been quite few studied. In this paper, a novel level permutation method for constructing uniform mixed-level designs is proposed. Our main idea is to perform level permutations on a new class of designs, called minimum average discrepancy designs, rather than generalized minimum aberration designs as in the fixed-level case. Several theoretical results on the design optimality and construction are obtained. Numerical results suggest the good performance of the resulting designs under various popular discrepancies.

Suggested Citation

  • Bochuan Jiang & Fei Wang & Yaping Wang, 2022. "Construction of uniform mixed-level designs through level permutations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 753-770, August.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:6:d:10.1007_s00184-021-00850-1
    DOI: 10.1007/s00184-021-00850-1
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    References listed on IDEAS

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    1. A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.
    2. Yan Liu & Min-Qian Liu, 2012. "Construction of equidistant and weak equidistant supersaturated designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 33-53, January.
    3. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
    4. Yong-Dao Zhou & Hongquan Xu, 2014. "Space-Filling Fractional Factorial Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1134-1144, September.
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