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Some lower bounds of centered $$L_2$$ L 2 -discrepancy of $$2^{s-k}$$ 2 s - k designs and their complementary designs

Author

Listed:
  • Zujun Ou
  • Hong Qin
  • Hongyi Li

Abstract

The indicator function is an effective tool in studying factorial designs. This paper presents some lower bounds of centered $$L_2$$ L 2 -discrepancy through indicator function. Some new lower bounds of centered $$L_2$$ L 2 -discrepancy for $$2^{s-k}$$ 2 s - k designs and their complementary designs are given. Numerical results show that our lower bounds are tight and better than the existing results. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Zujun Ou & Hong Qin & Hongyi Li, 2015. "Some lower bounds of centered $$L_2$$ L 2 -discrepancy of $$2^{s-k}$$ 2 s - k designs and their complementary designs," Statistical Papers, Springer, vol. 56(4), pages 969-979, November.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:969-979
    DOI: 10.1007/s00362-014-0618-2
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    References listed on IDEAS

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    1. 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.
    2. Ou, Zujun & Qin, Hong, 2010. "Some applications of indicator function in two-level factorial designs," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 19-25, January.
    3. N. Balakrishnan & Po Yang, 2011. "Forms of four-word indicator functions with implications to two-level factorial designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 375-386, April.
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