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Uniform minimum moment aberration designs

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

Abstract

This paper discusses the issue of constructing uniform minimum moment aberration designs under discrepancies criteria. By considering all possible level permutations of factors, we establish a linear relationship between power moments and average discrepancy defined by a reproducing kernel for an asymmetrical or symmetrical design. We prove that minimum moment aberration designs often have low average discrepancies. Moreover, the average centered L2-discrepancy is expressed as a linear combination of power moments for a given design. An efficient method for constructing uniform minimum moment aberration designs is proposed. Some asymmetrical uniform minimum moment aberration designs obtained by our method have low centered L2-discrepancy and can be recommended for use in practice.

Suggested Citation

  • Yang, Xue & Yang, Gui-Jun & Su, Ya-Juan, 2018. "Uniform minimum moment aberration designs," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 26-33.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:26-33
    DOI: 10.1016/j.spl.2017.12.005
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    References listed on IDEAS

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    1. Kashinath Chatterjee & Kai-Tai Fang & Hong Qin, 2006. "A Lower Bound for the Centered L 2 -Discrepancy on Asymmetric Factorials and its Application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 243-255, April.
    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.
    3. Yang, Xue & Chen, Hao & Liu, Min-Qian, 2014. "Resolvable orthogonal array-based uniform sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 108-115.
    Full references (including those not matched with items on IDEAS)

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