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Invariance of generalized wordlength patterns

Authors
Journal
Journal of Statistical Planning and Inference
0378-3758
Publisher
Elsevier
Publication Date
Volume
139
Issue
8
Identifiers
DOI: 10.1016/j.jspi.2008.12.005
Keywords
  • Fractional Factorial Design
  • Group Character
  • Hamming Weight
  • Multiset
  • Orthogonal Array
Disciplines
  • Design

Abstract

Abstract The generalized wordlength pattern (GWLP) introduced by Xu and Wu [2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist. 29, 1066–1077] for an arbitrary fractional factorial design allows one to extend the use of the minimum aberration criterion to such designs. Ai and Zhang [2004. Projection justification of generalized minimum aberration for asymmetrical fractional factorial designs. Metrika 60, 279–285] defined the J -characteristics of a design and showed that they uniquely determine the design. While both the GWLP and the J -characteristics require indexing the levels of each factor by a cyclic group, we see that the definitions carry over with appropriate changes if instead one uses an arbitrary abelian group. This means that the original definitions rest on an arbitrary choice of group structure. We show that the GWLP of a design is independent of this choice, but that the J -characteristics are not. We briefly discuss some implications of these results.

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