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Uniform augmented q-level designs

Author

Listed:
  • Zongyi Hu

    (Hunan University)

  • Jiaqi Liu

    (Hunan University)

  • Yi Li

    (Hunan University)

  • Hongyi Li

    (Jishou University)

Abstract

In many practical applications, follow-up experimental designs are commonly used to explore the relationship between inputs and outputs steps by steps. As some additional resources could be available to the experimenter after the first step, some additional runs or factors may be added in the follow-up stage. The issue of uniform augmented q-level designs is investigated in this paper. Using the level permutation technique, the uniformity of augmented q-level designs is discussed under the average mixture discrepancy, and new lower bounds of average mixture discrepancy for augmented designs are obtained, which can be served as the benchmark for searching uniform augmented designs. Numerical examples show that the uniform augmented designs can be constructed with high efficiency.

Suggested Citation

  • Zongyi Hu & Jiaqi Liu & Yi Li & Hongyi Li, 2021. "Uniform augmented q-level designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 969-995, October.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:7:d:10.1007_s00184-020-00793-z
    DOI: 10.1007/s00184-020-00793-z
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    References listed on IDEAS

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    1. Zujun Ou & Hong Qin, 2019. "Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy," Statistical Papers, Springer, vol. 60(5), pages 1699-1716, October.
    2. Chen, Wen & Qi, Zong-Feng & Zhou, Yong-Dao, 2015. "Constructing uniform designs under mixture discrepancy," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 76-82.
    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. Yong-Dao Zhou & Kai-Tai Fang, 2013. "An efficient method for constructing uniform designs with large size," Computational Statistics, Springer, vol. 28(3), pages 1319-1331, June.
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