UNIFORM PROJECTION DESIGNS

• 成果类型: Article
• 署名作者: Sun, Fasheng; Wang, Yaping; Xu, Hongquan
• 署名单位: Northeast Normal University - China; Northeast Normal University - China; East China Normal University; University of California System; University of California Los Angeles
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1705
• 发表日期: 2019
• 页码: 641-661
• 关键词: strong orthogonal arrays; latin hypercubes; Connection

摘要

Efficient designs are in high demand in practice for both computer and physical experiments. Existing designs (such as maximin distance designs and uniform designs) may have bad low-dimensional projections, which is undesirable when only a few factors are active. We propose a new design criterion, called uniform projection criterion, by focusing on projection uniformity. Uniform projection designs generated under the new criterion scatter points uniformly in all dimensions and have good space-filling properties in terms of distance, uniformity and orthogonality. We show that the new criterion is a function of the pairwise L-1-distances between the rows, so that the new criterion can be computed at no more cost than a design criterion that ignores projection properties. We develop some theoretical results and show that maximin L-1-equidistant designs are uniform projection designs. In addition, a class of asymptotically optimal uniform projection designs based on good lattice point sets are constructed. We further illustrate an application of uniform projection designs via a multidrug combination experiment.