Construction of optimal multi-level supersaturated designs

• 成果类型: Article
• 署名作者: Xu, HQ; Wu, CFJ
• 署名单位: University of California System; University of California Los Angeles; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000688
• 发表日期: 2005
• 页码: 2811-2836
• 关键词: fractional factorial-designs; generalized minimum aberration; orthogonal arrays; projection justification; g(2)-aberration

摘要

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman-Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.