On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments. Issue 537 (2nd January 2022)

• Record Type: Journal Article
• Authors: Wang, Yaping; Sun, Fasheng; Xu, Hongquan
• Is Part Of: Journal of the American Statistical Association. Volume 117:Issue 537(2022)
• Page Start: 375
• Page End: 385
• Publication Date: 2022-01-02
• Subjects: Correlation -- Latin hypercube design -- Lp-distance -- Space-filling property -- Uniform projection designs; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2020.1782221
• Languages: English
• ISSNs: 0162-1459

Abstract

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 L 2 -distances between the rows only. We further explore the connection between uniform projection designs and maximin L 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. Supplementary materials for this article are available online.