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Asymmetric uniform designs based on mixture discrepancy

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  • A. M. Elsawah
  • Hong Qin

Abstract

Efficient experimental design is crucial in the study of scientific problems. The uniform design is one of the most widely used approaches. The discrepancies have played an important role in quasi-Monte Carlo methods and uniform design. Zhou et al. [17] proposed a new type of discrepancy, mixture discrepancy ( $ {\mathcal {MD}} $ MD), and showed that $ {\mathcal {MD}} $ MD may be a better uniformity measure than other discrepancies. In this paper, we discuss in depth the $ {\mathcal{MD}} $ MD as the uniformity measure for asymmetric mixed two and three levels U-type designs. New analytical expression based on row distance and new lower bound of the $ {\mathcal {MD}} $ MD are given for asymmetric levels designs. Using the new formulation and the new lower bound as the benchmark, we can implement a new version of the fast local search heuristic threshold accepting. By this search heuristic, we can obtain mixed two and three levels U-type designs with low discrepancy.

Suggested Citation

  • A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.
  • Handle: RePEc:taf:japsta:v:43:y:2016:i:12:p:2280-2294
    DOI: 10.1080/02664763.2016.1140727
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    References listed on IDEAS

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    1. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    2. Elsawah, A.M. & Qin, Hong, 2015. "A new strategy for optimal foldover two-level designs," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 116-126.
    3. Elsawah, A.M. & Qin, Hong, 2015. "Mixture discrepancy on symmetric balanced designs," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 123-132.
    4. Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.
    5. 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. Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
    2. A. M. Elsawah & Kai-Tai Fang, 2018. "New results on quaternary codes and their Gray map images for constructing uniform designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 307-336, April.
    3. Bochuan Jiang & Fei Wang & Yaping Wang, 2022. "Construction of uniform mixed-level designs through level permutations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 753-770, August.
    4. A. M. Elsawah & Kai-Tai Fang & Xiao Ke, 2021. "New recommended designs for screening either qualitative or quantitative factors," Statistical Papers, Springer, vol. 62(1), pages 267-307, February.

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