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Discrete discrepancy in factorial designs

Author

Listed:
  • Hong Qin
  • Kai-Tai Fang

Abstract

Discrepancy measure can be utilized as a uniformity measure for comparing factorial designs. A so-called discrete discrepancy has been used to evaluate the uniformity of factorials. In this paper we give linkages among uniformity measured by the discrete discrepancy, generalized minimum aberration, minimum moment aberration and uniformity measured by the centered L 2 -discrepancy/the wrap-around L 2 -discrepancy. These close linkages provide a significant justification for the discrete discrepancy used to measure uniformity of factorial designs. Copyright Springer-Verlag 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:60:y:2004:i:1:p:59-72
    DOI: 10.1007/s001840300296
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    Citations

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    Cited by:

    1. Li, Hongyi & Chatterjee, Kashinath & Li, Bo & Qin, Hong, 2016. "Construction of Sudoku-based uniform designs with mixed levels," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 111-118.
    2. 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.
    3. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    4. Rong-Xian Yue & Kashinath Chatterjee, 2010. "Bayesian U-type design for nonparametric response surface prediction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 219-231, September.
    5. Fasheng Sun & Jie Chen & Min-Qian Liu, 2011. "Connections between uniformity and aberration in general multi-level factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 305-315, May.
    6. Liuping Hu & Zujun Ou & Hongyi Li, 2020. "Construction of four-level and mixed-level designs with zero Lee discrepancy," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 129-139, January.
    7. Biao Luo & Hongyi Li & Yingying Wei & Zujun Ou, 2022. "Uniform design with prior information of factors under weighted wrap-around $$L_2$$ L 2 -discrepancy," Computational Statistics, Springer, vol. 37(5), pages 2717-2739, November.
    8. Chatterjee, Kashinath & Qin, Hong, 2008. "A new look at discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2988-2991, December.
    9. Hong Qin & Na Zou & Kashinath Chatterjee, 2009. "Connection between uniformity and minimum moment aberration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 79-88, June.

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