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Level-augmented uniform designs

Author

Listed:
  • Yan-Ping Gao

    (Nankai University)

  • Si-Yu Yi

    (Nankai University)

  • Yong-Dao Zhou

    (Nankai University)

Abstract

Most of existing augmented designs are to add some runs in the follow-up stages. While in many cases, the level of factors should be augmented and these augmented designs are called level-augmented designs. According to whether the experimental domain is extended or not, they can be divided into range-extended and range-fixed level-augmented designs. For different types of initial designs, the symmetrical and asymmetrical level-augmented designs are discussed, respectively. Based on the property of robustness, a uniformity criterion is a suitable choice to obtain an optimal level-augmented design when the model is unknown. In this paper, the wrap-around $$L_2$$ L 2 -discrepancy (WD) is chosen as the uniformity measure. We give the expressions and the tight lower bounds of WD of level-augmented designs under some special parameters. A method to construct a special case of symmetrical level-augmented designs is given. Some examples and level-augmented uniform designs are also provided.

Suggested Citation

  • Yan-Ping Gao & Si-Yu Yi & Yong-Dao Zhou, 2022. "Level-augmented uniform designs," Statistical Papers, Springer, vol. 63(2), pages 441-460, April.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:2:d:10.1007_s00362-021-01247-y
    DOI: 10.1007/s00362-021-01247-y
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    References listed on IDEAS

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    1. 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.
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