Oracle arrays and their use for constructing space-filling designs

• 成果类型: Article; Early Access
• 署名作者: Tang, Boxin
• 署名单位: Simon Fraser University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag075
• 发表日期: 2026-05-19
• 关键词: computer experiment; Hamming distance; level permutation; maximin distance design; minimum G(2)-aberration; resolvable balanced incomplete block design; generalized minimum aberration; LATIN HYPERCUBE DESIGNS; projection justification

摘要

The maximin distance is an attractive criterion for constructing space-filling designs. As factors in computer experiments are generally quantitative, the L-p-distance is appropriate. Theoretical construction of maximin L-p-distance designs, however, is extremely challenging. Given that directly attacking the problem is difficult, we propose an indirect approach that first constructs maximin Hamming distance designs and then constructs maximin L-p-distance designs using the former. The approach turns out to be very fruitful. We introduce oracle arrays, which are a special class of maximin Hamming distance arrays that also allow other maximin Hamming distance arrays to be easily constructed. We then examine how to use oracle arrays to construct maximin L-p-distance designs. Although the approach is motivated by the desire of constructing maximin L-p-distance designs, it can also be thought of as a generalization of the idea of orthogonal array based designs.