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Generalized \(E(s^{2})\) criterion for multilevel supersaturated designs. (English) Zbl 1177.62091
Summary: Several extensions of the popular \(E(s^{2})\) criterion of K. H. V. Booth and D. R. Cox [Technometrics 4, 489–495 (1962; Zbl 0109.12201)] to multilevel supersaturated designs have been advanced in the literature. These extensions are not unique due to different ways they measure overall non-orthogonality between all pairs of the columns of the model matrix. We exploit the connection of the \(E(s^{2})\) criterion with \(A\)- and \(D\)-optimality that naturally lends itself to a generalized criterion for the multilevel situation in a unified way. The extensions provided in the literature follow as special cases of the generalized criterion. A lower bound to the generalized criterion is derived for a wide class of designs, and a method of construction for the symmetrical case is discussed.

MSC:
62K05 Optimal statistical designs
62K15 Factorial statistical designs
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