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Constructing uniform designs under mixture discrepancy

Author

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  • Chen, Wen
  • Qi, Zong-Feng
  • Zhou, Yong-Dao

Abstract

The discrepancies have played an important role in quasi-Monte Carlo methods and uniform design. Zhou et al. (2013) proposed a new type of discrepancy, mixture discrepancy (MD), and showed that MD may be a better uniformity measure than wrap-around L2-discrepancy and centered L2-discrepancy. In this paper, some constructing methods for uniform designs under MD are shown. The relationship between MD and the generalized wordlength pattern for multi-level design is given, then the level permutation technique is shown as a useful tool to search uniform designs. Moreover, it is shown that MD can be represented by quadratic form and the global optimum solution of experimental design under MD is also given. Furthermore, by such quadratic form, the relationship between a design and its complementary design is shown, which can be used to construct uniform design with large size.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:76-82
    DOI: 10.1016/j.spl.2014.11.007
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    References listed on IDEAS

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    1. Hongquan Xu, 2005. "A catalogue of three-level regular fractional factorial designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(2), pages 259-281, November.
    2. 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. 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.
    2. 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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