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Constructing optimal asymmetric combined designs via Lee discrepancy

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  • Elsawah, A.M.

Abstract

The main objective of the present paper is to provide an answer to the question: How to construct optimal combined designs, whether regular or nonregular? In this paper, we take the Lee discrepancy as the optimality measure to construct the optimal mixed levels combined designs, which are most commonly used in practice. Equivalence between any combined design and its complementary combined design is investigated, which is a very useful constraint that reduce the search space for the optimal combined designs.

Suggested Citation

  • Elsawah, A.M., 2016. "Constructing optimal asymmetric combined designs via Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 24-31.
    • Handle: RePEc:eee:stapro:v:118:y:2016:i:c:p:24-31
    DOI: 10.1016/j.spl.2016.06.008
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Elsawah, A.M. & Qin, Hong, 2015. "Mixture discrepancy on symmetric balanced designs," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 123-132.
    4. Elsawah, A.M. & Qin, Hong, 2015. "Lee discrepancy on symmetric three-level combined designs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 273-280.
    5. 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.
    6. 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.
    7. Elsawah, A.M. & Qin, Hong, 2014. "New lower bound for centered L2-discrepancy of four-level U-type designs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 65-71.
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    Cited by:

    1. A. M. Elsawah, 2018. "Choice of optimal second stage designs in two-stage experiments," Computational Statistics, Springer, vol. 33(2), pages 933-965, June.
    2. A. M. Elsawah & Kai-Tai Fang, 2020. "New foundations for designing U-optimal follow-up experiments with flexible levels," Statistical Papers, Springer, vol. 61(2), pages 823-849, April.
    3. A. M. Elsawah & Kai-Tai Fang & Ping He & Hong Qin, 2021. "Sharp lower bounds of various uniformity criteria for constructing uniform designs," Statistical Papers, Springer, vol. 62(3), pages 1461-1482, June.

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