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.