99-26
Kiefer Ordering of Second-Degree Mixture Designs for Four Ingredients
by Draper, N. R.; Heiligers, B.; Pukelsheim, F.
Preprint series: 99-26, Preprints
- MSC:
- 62K99 None of the above but in this section
- 62J05 Linear regression
- 15A69 Multilinear algebra, tensor products
- 15A45 Miscellaneous inequalities involving matrices
Abstract: For quadratic mixture models on the simplex, we discuss the improvement of a given design in terms of increasing symmetry, as well as obtaining a larger moment matrix under the Loewner ordering. The two criteria together define the Kiefer design ordering. The Kiefer ordering can be discussed in the usual Scheff\xe9 model algebra, or in the alternative Kronecker product algebra. We employ the Kronecker algebra which reflects the symmetries of the simplex experiment region. We show that the set of weighted centroid designs constitutes a convex complete class for the Kiefer ordering. For four ingredients, the class is minimal complete.
Keywords: Complete class results, Exchangeable designs, Kiefer design ordering, Kronecker product, Majorization, Scheff\xe9 canonical polynomials, Weighted centroid designs.
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