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Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy

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  • Zujun Ou

    (Jishou University)

  • Hong Qin

    (Central China Normal University)

Abstract

Literatures reveal that foldover is a useful technique in construction of factorial designs. The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around $$L_2$$ L 2 -discrepancy to assess the optimal foldover plans for asymmetric fractional factorials. A general foldover strategy and combined design under a foldover plan are developed for asymmetric fractional factorials, some theoretical properties on the equivalence between the defined foldover plan and its complementary foldover plan are discussed. A new lower bound for the wrap-around $$L_2$$ L 2 -discrepancy of combined designs is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.

Suggested Citation

  • Zujun Ou & Hong Qin, 2019. "Optimal foldover plans of asymmetric factorials with minimum wrap-around $$L_2$$ L 2 -discrepancy," Statistical Papers, Springer, vol. 60(5), pages 1699-1716, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0892-x
    DOI: 10.1007/s00362-017-0892-x
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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. Peng-Fei Li & Min-Qian Liu & Run-Chu Zhang, 2005. "Choice of optimal initial designs in sequential experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 127-135, April.
    3. 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.
    4. Fang, Kai-Tai & Lin, Dennis K. J. & Qin, Hong, 2003. "A note on optimal foldover design," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 245-250, April.
    5. Zujun Ou & Kashinath Chatterjee & Hong Qin, 2011. "Lower bounds of various discrepancies on combined designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 109-119, July.
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    Cited by:

    1. Zujun Ou & Hongyi Li, 2021. "A new foldover strategy and optimal foldover plans for three-level design," Statistical Papers, Springer, vol. 62(5), pages 2433-2451, October.
    2. 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.

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