2-level Fractional Factorial Designs which are the Union of Non Trivial Regular Designs
Article
First Online:
Received:
Revised:
Abstract
Each non regular fraction of a 2-level factorial design is a union of points, each of them being trivially a regular fraction. In order to find non-trivial decompositions of non regular fractions into regular fractions, in the first part of the paper we derive a condition for the inclusion of a regular fraction in a generic fraction. We use polynomial algebra arguments introduced by the authors and Maria Piera Rogantin (JSPI, 2000). The practical interest of the decomposition and its computational feasibility are discussed in the second part of the paper.
AMS Subject Classification
62K15Keywords
2-level factorial design Plackett-Burman design Algebraic statistics Indicator polynomialPreview
Unable to display preview. Download preview PDF.
References
- Carlini, E., Pistone, G., 2007. Hibert bases for orthogonal arrays. Journal of Statistical Theory and Practice, 1 (3–4), 299–309.MathSciNetCrossRefGoogle Scholar
- CoCoATeam, online. CoCoA: a system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it.Google Scholar
- Cox, D., Little, J., O’Shea, D., 1997. Ideals, Varieties, and Algorithms, 2nd edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York, an introduction to computational algebraic geometry and commutative algebra.zbMATHGoogle Scholar
- Fontana, R., Pistone, G., Rogantin, M., May 2000. Classification of two-level factorial fractions. Journal of Statistical Planning and Inference, 87 (1), 149–172.MathSciNetCrossRefGoogle Scholar
- GAP, 2007. GAP — Groups, Algorithms, and Programming, Version 4.4.10. The GAP Group. Available at http://www.gap-system.org Google Scholar
- Gibilisco, P., Riccomagno, E., Rogantin, M., Wynn, H. P. (editors), 2009. Algebraic and Geometric Methods in Statistics. Cambridge University Press.Google Scholar
- Hedayat, A. S., Sloane, N. J. A., Stufken, J., 1999. Orthogonal Arrays. Theory and Applications. Springer Series in Statistics. Springer-Verlag, New York.CrossRefGoogle Scholar
- Kreuzer, M., Robbiano, L., 2000. Computational Commutative Algebra. 1. Springer-Verlag, Berlin.CrossRefGoogle Scholar
- Notari, R., Riccomagno, E., Rogantin, M., 2007. Two polynomial representations of experimental design. Journal of Statistical Theory and Practice, 1 (3–4), 329–346.MathSciNetCrossRefGoogle Scholar
- Pistone, G., Riccomagno, E., Rogantin, M., 2007. Algebraic statistics for the design of experiments. In Search for Optimality in Design and Statistics: Algebraic and Dynamical System Methods, Pronzato, L., Zigljavsky, A.A. (editors). Springer-Verlag, pp. 95–129.Google Scholar
- Pistone, G., Riccomagno, E., Wynn, H.P., 2001. Algebraic statistics. Computational Commutative Algebra in Statistics. Vol. 89 of Monographs on Statistics and Applied Probability, Chapman & Hall/CRC, Boca Raton, FL.zbMATHGoogle Scholar
- Pistone, G., Rogantin, M., 2008. Indicator function and complex coding for mixed fractional factorial designs. J. Statist. Plann. Inference, 138 (3), 787–802.MathSciNetCrossRefGoogle Scholar
- Pistone, G., Rogantin, M., 2009. Regular fractions and indicator polynomials. Rapporti Interni, 2009/8, Politecnico di Torino DIMAT.Google Scholar
- Plackett, R., Burman, J., 1946. The design of optimum multifactorial experiments. Biometrika, 33, 305–325.MathSciNetCrossRefGoogle Scholar
- Ye, K. Q., 2003. Indicator function and its application in two-level factorial designs. The Annals of Statistics, 31 (3), 984–994.MathSciNetCrossRefGoogle Scholar
Copyright information
© Grace Scientific Publishing 2010