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On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments

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  • Yaping Wang
  • Fasheng Sun
  • Hongquan Xu

Abstract

Space-filling designs are widely used in both computer and physical experiments. Column-orthogonality, maximin distance, and projection uniformity are three basic and popular space-filling criteria proposed from different perspectives, but their relationships have been rarely investigated. We show that the average squared correlation metric is a function of the pairwise L2-distances between the rows only. We further explore the connection between uniform projection designs and maximin L1-distance designs. Based on these connections, we develop new lower and upper bounds for column-orthogonality and projection uniformity from the perspective of distance between design points. These results not only provide new theoretical justifications for each criterion but also help in finding better space-filling designs under multiple criteria. Supplementary materials for this article are available online.

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  • Yaping Wang & Fasheng Sun & Hongquan Xu, 2022. "On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 375-385, January.
    • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:537:p:375-385
    DOI: 10.1080/01621459.2020.1782221
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    Cited by:

    1. Bing Guo & Xiao-Rong Li & Min-Qian Liu & Xue Yang, 2023. "Construction of orthogonal general sliced Latin hypercube designs," Statistical Papers, Springer, vol. 64(3), pages 987-1014, June.
    2. Weiyan Mu & Chengxin Liu & Shifeng Xiong, 2023. "Nested Maximum Entropy Designs for Computer Experiments," Mathematics, MDPI, vol. 11(16), pages 1-12, August.

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