UNIFORM PROJECTION DESIGNS

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

来源：Annals of Statistics, 2019, 47(1): 641-661.

DOI：10.1214/18-AOS1705

• Computer experiment
• discrepancy
• Latin hypercube design
• maximin distance design
• space-filling design
• uniform design

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.

• 出版日期2019-2
• 单位东北师范大学; 华东师范大学