A stratified L2-discrepancy with application to space-filling designs

• 成果类型: Article; Early Access
• 署名作者: Tian, Ye; Xu, Hongquan
• 署名单位: Beijing University of Posts & Telecommunications; University of California System; University of California Los Angeles
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf055
• 发表日期: 2025
• 关键词: strong orthogonal arrays; discrepancy

摘要

Space-filling designs are widely used in computer experiments. We propose a stratified L2-discrepancy to evaluate the uniformity of a design when the design domain is stratified into various subregions. Weights are used to adjust preferences for the uniformity over subregions in each stratification. The stratified L2-discrepancy is easy to compute, satisfies a Koksma-Hlawka type inequality, and overcomes the curse of dimensionality that exists for other discrepancies. It is applicable to a broad class of designs, and covers several minimum aberration-type criteria as special cases. Strong orthogonal arrays of maximum strength are shown to have low stratified L2-discrepancies, and thus are suitable for computer experiments. In addition, we develop a lower bound for the stratified L2-discrepancy and provide a construction method for designs that achieve the lower bound. We further introduce a general version of the stratified L2-discrepancy for evaluating designs with flexible stratification properties.