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Lee discrepancy on symmetric three-level combined designs

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  • Elsawah, A.M.
  • Qin, Hong

Abstract

This article develops a new mechanism to foldover designs involving factors with multi-level. By exhaustive search we identify the optimal foldover plans. This paper aims to study the issue of the optimal foldover plans for three-level designs, in view of the uniformity criterion measured by the Lee discrepancy.

Suggested Citation

  • Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:273-280
    DOI: 10.1016/j.spl.2014.09.027
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    References listed on IDEAS

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    1. 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.
    2. Zujun Ou & Hong Qin & Xu Cai, 2014. "A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2274-2285, May.
    3. 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.
    4. Chatterjee, Kashinath & Li, Zhaohai & Qin, Hong, 2012. "Some new lower bounds to centered and wrap-round L2-discrepancies," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1367-1373.
    5. Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing, 2008. "Lee discrepancy and its applications in experimental designs," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1933-1942, September.
    6. 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. Elsawah, A.M. & Qin, Hong, 2015. "Mixture discrepancy on symmetric balanced designs," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 123-132.
    2. Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
    3. Zou, Na & Gou, Tingxun & Qin, Hong & Chatterjee, Kashinath, 2020. "Generalized foldover method for high-level designs," Statistics & Probability Letters, Elsevier, vol. 164(C).
    4. Elsawah, A.M. & Qin, Hong, 2015. "A new strategy for optimal foldover two-level designs," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 116-126.
    5. A. M. Elsawah & Hong Qin, 2016. "Asymmetric uniform designs based on mixture discrepancy," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2280-2294, September.

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