by Draper, N. R., Heiligers, B., Pukelsheim, F..
Series: 1999-26, Preprints
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.
Complete class results, Exchangeable designs, Kiefer design ordering, Kronecker product, Majorization, Scheffé canonical polynomials, Weighted centroid designs.