Geometric isomorphism and minimum aberration for factorial designs with quantitative factors

Annals of Statistics

Volumn 32, Issue 5, 2004, Pages 2168-2185

  Cheng, Shao Wei ^a,c   Ye, Kenny Q ^b  

^a ACADEMIA SINICA   (Taiwan)

^b ALBERT EINSTEIN COLLEGE OF MEDICINE   (United States)

^c INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Generalized wordlength pattern; Indicator function; Polynomial models

Indexed keywords

EID: 12344337993     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000000599     Document Type: Article

References (13)

1. CHENG, S.-W. and Wu, C.-F. J. (2001). Factor screening and response surface exploration (with discussion). Statist. Sinica 11 553-604.
2. DRAPER, N. R. and SMITH, H. (1998). Applied Regression Analysis, 3rd ed. Wiley, New York.
3. k-p designs. Technometrics 22 601-608.
4. FONTANA, R., PISTONE, G. and ROGANTIN, M. P. (2000). Classification of two-level factorial fractions. J. Statist. Plann. Inference 87 149-172.
5. KENNEDY, W. J., JR. and GENTLE, J. E. (1980). Statistical Computing. Dekker, New York.
6. PISTONE, G., RICCOMAGNO, E. and WYNN, H. P. (2000). Algebraic Statistics: Computational Commutative Algebra in Statistics. Chapman and Hall, Boca Raton.
7. PISTONE, G. and WYNN, H. P. (1996). Generalized confounding with Gröbner bases. Biometrika 83 653-666.
8. 2-aberration for nonregular fractional factorial designs. Ann. Statist. 27 1914-1926.
9. WANG, J. C. and Wu, C.-F. J. (1995). A hidden projection property of Plackett-Burman and related designs. Statist. Sinica 5 235-250.
10. WU, C.-F. J. and HAMADA, M. (2000). Experiments: Planning, Analysis and Parameter Design Optimization. Wiley, New York.
11. XU, H. and WU, C.-F. J. (2001). Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist. 29 1066-1077.
12. YE, K. Q. (1999). Geometric aliasing, generalized defining relations, and Groebner basis: A new look at multi-level factorial designs. Unpublished manuscript.
13. YE, K. Q. (2003). Indicator function and its application in two-level factorial designs. Ann. Statist. 31 984-994.