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

Xue Yang, Gui-Jun Yang and Ya-Juan Su

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 4, 995-1008

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.

Date: 2019
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DOI: 10.1080/03610926.2017.1422761

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