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Lower bound of average centered L2${\bm L_2}$-discrepancy for U${\bm U}$-type designs

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  • Xue Yang
  • Gui-Jun Yang
  • Ya-Juan Su

Abstract

Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L2-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L2-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.

Suggested Citation

  • Xue Yang & Gui-Jun Yang & Ya-Juan Su, 2019. "Lower bound of average centered L2${\bm L_2}$-discrepancy for U${\bm U}$-type designs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(4), pages 995-1008, February.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:4:p:995-1008
    DOI: 10.1080/03610926.2017.1422761
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