The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 2 (2005), 944-958.
A general theory of minimum aberration and its applications
Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.
Ann. Statist., Volume 33, Number 2 (2005), 944-958.
First available in Project Euclid: 26 May 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62K15: Factorial designs
Cheng, Ching-Shui; Tang, Boxin. A general theory of minimum aberration and its applications. Ann. Statist. 33 (2005), no. 2, 944--958. doi:10.1214/009053604000001228. https://projecteuclid.org/euclid.aos/1117114341