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Design efficiency for minimum projection uniform designs with q levels

Author

Listed:
  • Qiming Bai

    (Jishou University)

  • Hongyi Li

    (Jishou University)

  • Xingyou Huang

    (Jishou University)

  • Huili Xue

    (Jishou University)

Abstract

Minimum projection uniform designs and high efficient designs are two kinds of excellent designs in design of experiment. In this paper, design efficiency for minimum projection uniform designs with q levels is discussed. Firstly, the uniformity pattern of q-level designs is proposed based on the centered $$L_2$$ L 2 -discrepancy. Secondly, the analytical connection between uniformity pattern and design efficiency is established for the q-level orthogonal arrays with strength 2, and for the orthogonal arrays with strength 3, the minimum projection uniformity criterion is equivalent to the design efficiency criterion. Finally, a tight lower bound of uniformity pattern is presented, which is used as a benchmark for measuring the uniformity of projection designs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:5:d:10.1007_s00184-022-00885-y
    DOI: 10.1007/s00184-022-00885-y
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    References listed on IDEAS

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    1. 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.
    2. Yi, Si-Yu & Zhou, Yong-Dao, 2018. "Projection uniformity under mixture discrepancy," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 96-105.
    3. Liuping Hu & Kashinath Chatterjee & Jiaqi Liu & Zujun Ou, 2020. "New lower bound for Lee discrepancy of asymmetrical factorials," Statistical Papers, Springer, vol. 61(4), pages 1763-1772, August.
    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. Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
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