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1999-26

Kiefer Ordering of Second-Degree Mixture Designs for Four Ingredients

by Draper, N. R., Heiligers, B., Pukelsheim, F..


Series: 1999-26, 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 Scheffé 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, Scheffé canonical polynomials, Weighted centroid designs.