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Projection justification of generalized minimum aberration for asymmetrical fractional factorial designs. (English) Zbl 1083.62071

Summary: Recently, H. Xu and C. F. J. Wu [Ann. Stat. 29, No. 4, 1066–1077 (2001; Zbl 1041.62067)] presented a generalized minimum aberration criterion for comparing and selecting general fractional factorial designs. This criterion is defined using a set of \(\chi_u(D)\) values, called \(J\)-characteristics by us. We find a set of linear equations that relate the set of design points to that of \(J\)-characteristics, which implies that a factorial design is uniquely determined by its \(J\)-characteristics once the orthonormal contrasts are designated. Thereto, a projection justification of generalized minimum aberration is established. All of these conclusions generalize the results for two-level symmetrical factorial designs of B. Tang [Biometrika 88, No. 2, 401–407 (2001; Zbl 0984.62053)].

MSC:

62K15 Factorial statistical designs
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