2005/12/01 by Hongquan Xu, C. F. J. Wu, Cfj Wu
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Optimal Experimental Design Methods #math.ST #msc:05B15 #msc:62K05 #msc:62K15 #stat.TH
paper · pdf · doi:10.1214/009053605000000688
published as Annals of Statistics 2005, Vol. 33, No. 6, 2811-2836 · Published at http://dx.doi.org/10.1214/009053605000000688 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2005/12/01 · arxiv created 2006/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.