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.
Publication:
Journal of the American Statistical Association, 2022, Vol. 117, No. 537, 375–385
Author:
Yaping Wang
KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai 200062, China
Fasheng Sun
KLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, China
Hongquan Xu
Department of Statistics, University of California, Los Angeles, CA 90095, USA