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Uniformity pattern of q-level factorials under mixture discrepancy

Author

Listed:
  • Kang Wang

    (Jishou University)

  • Zujun Ou

    (Jishou University)

  • Jiaqi Liu

    (Hunan University)

  • Hongyi Li

    (Jishou University)

Abstract

The objective of this paper is to discuss the issue of the projection uniformity of factorial designs measured by mixture discrepancy. The average projection discrepancy of combinatorially isomorphic designs obtained by level permutation on each factor is defined, which measures the projection uniformity on different dimensions. The uniformity pattern and minimum projection uniformity criterion for selecting optimal design are defined for q-level designs. The relationships between uniformity pattern, orthogonality and generalized word-length pattern are built. Moreover, a tight lower bound of uniformity pattern is also obtained.

Suggested Citation

  • Kang Wang & Zujun Ou & Jiaqi Liu & Hongyi Li, 2021. "Uniformity pattern of q-level factorials under mixture discrepancy," Statistical Papers, Springer, vol. 62(4), pages 1777-1793, August.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:4:d:10.1007_s00362-019-01155-2
    DOI: 10.1007/s00362-019-01155-2
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    References listed on IDEAS

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    1. Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
    2. Yi, Si-Yu & Zhou, Yong-Dao, 2018. "Projection uniformity under mixture discrepancy," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 96-105.
    3. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    4. Zhang, Shangli & Qin, Hong, 2006. "Minimum projection uniformity criterion and its application," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 634-640, March.
    5. Zhenghong Wang & Hong Qin, 2018. "Uniformity pattern and related criteria for mixed-level designs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3192-3203, July.
    6. 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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    Cited by:

    1. Qiming Bai & Hongyi Li & Shixian Zhang & Jiezhong Tian, 2023. "Design Efficiency of the Asymmetric Minimum Projection Uniform Designs," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    2. Qiming Bai & Hongyi Li & Xingyou Huang & Huili Xue, 2023. "Design efficiency for minimum projection uniform designs with q levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 577-594, July.

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