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

• 成果类型: Article
• 署名作者: Wang, Yaping; Sun, Fasheng; Xu, Hongquan
• 署名单位: East China Normal University; Northeast Normal University - China; Northeast Normal University - China; University of California System; University of California Los Angeles
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1782221
• 发表日期: 2022
• 页码: 375-385
• 关键词: space-filling designs; latin hypercubes; arrays

摘要

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.