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

作者：Wang, Yaping; Sun, Fasheng; Xu, Hongquan^*

来源：Journal of the American Statistical Association, 2022, 117(537): 375-385.

DOI：10.1080/01621459.2020.1782221

• Correlation
• Latin hypercube design
• L-p-distance
• Space-filling property
• Uniform projection designs

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 pairwiseL(2)-distances between the rows only. We further explore the connection between uniform projection designs and maximinL(1)-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.for this article are available online.