ON THE CONSTRUCTION OF NESTED SPACE-FILLING DESIGNS

• 成果类型: Article
• 署名作者: Sun, Fasheng; Liu, Min-Qian; Qian, Peter Z. G.
• 署名单位: Northeast Normal University - China; Northeast Normal University - China; Nankai University; Nankai University; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1229
• 发表日期: 2014
• 页码: 1394-1425
• 关键词: computer experiments; models

摘要

Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multifidelity computer models, stochastic optimization problems, multi-level fitting of nonparametric functions, and linking parameters. We propose methods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other algebraic techniques. The constructed designs can accommodate a nested structure with an arbitrary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed methods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors.