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Construction of mixed-level designs with minimum discrete discrepancy

Author

Listed:
  • Hu, Liuping
  • Chatterjee, Kashinath
  • Ning, Jianhui
  • Qin, Hong

Abstract

Mixed-level designs are widely applicable in various practical fields. In this paper, we introduce new methods for constructing mixed-level designs with minimum discrete discrepancy. Utilizing the minimum discrete discrepancy aberration criterion, we establish a valuable analytical connection between the initial design and the resultant design, demonstrating that a high-quality initial design ensures the quality of the resultant design. Additionally, we derive general lower bounds for the discrete discrepancy, which serve as benchmarks for assessing the uniformity of mixed-level designs. Examples are provided to illustrate the effectiveness of our construction methods and the significance of the newly derived lower bounds.

Suggested Citation

  • Hu, Liuping & Chatterjee, Kashinath & Ning, Jianhui & Qin, Hong, 2025. "Construction of mixed-level designs with minimum discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715225000045
    DOI: 10.1016/j.spl.2025.110358
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    References listed on IDEAS

    as
    1. Chatterjee, Kashinath & Qin, Hong, 2008. "A new look at discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2988-2991, December.
    2. Hong Qin & Kai-Tai Fang, 2004. "Discrete discrepancy in factorial designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 60(1), pages 59-72, July.
    3. Hongyi Li & Xingyou Huang & Huili Xue & Hong Qin, 2021. "A novel method for constructing mixed two- and three-level uniform factorials with large run sizes," Statistical Papers, Springer, vol. 62(6), pages 2907-2921, December.
    Full references (including those not matched with items on IDEAS)

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