Geometric isomorphism and minimum aberration for factorial designs with quantitative factors
成果类型：
Article
署名作者：
Cheng, SW; Ye, KQ
署名单位：
Academia Sinica - Taiwan; Montefiore Medical Center; Albert Einstein College of Medicine; Yeshiva University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053604000000599
发表日期：
2004
页码：
2168-2185
关键词：
摘要：
Factorial designs have broad applications in agricultural, engineering and scientific studies. In constructing and studying properties of factorial designs, traditional design theory treats all factors as nominal. However, this is not appropriate for experiments that involve quantitative factors. For designs with quantitative factors, level permutation of one or more factors in a design matrix could result in different geometric structures, and, thus, different design properties. In this paper indicator functions are introduced to represent factorial designs. A polynomial form of indicator functions is used to characterize the geometric structure of those designs. Geometric isomorphism is defined for classifying designs with quantitative factors. Based on indicator functions, a new aberration criteria is proposed and some minimum aberration designs are presented.