A CLASSIFICATION CRITERION FOR DEFINITIVE SCREENING DESIGNS

• 成果类型: Article
• 署名作者: Schoen, Eric D.; Eendebak, Pieter T.; Goos, Peter
• 署名单位: KU Leuven; Netherlands Organization Applied Science Research; University of Antwerp
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1723
• 发表日期: 2019
• 页码: 1179-1202
• 关键词: Matrices

摘要

A conference design is a rectangular matrix with orthogonal columns, one zero in each column, at most one zero in each row and -1's and +1's elsewhere. A definitive screening design can be constructed by folding over a conference design and adding a row vector of zeroes. We prove that, for a given even number of rows, there is just one isomorphism class for conference designs with two or three columns. Next, we derive all isomorphism classes for conference designs with four columns. Based on our results, we propose a classification criterion for definitive screening designs founded on projections into four factors. We illustrate the potential of the criterion by studying designs with 24 and 82 factors.