Abstract
For 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. For the second-degree mixture model, 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. Of essential importance for the derivation is a certain moment polytope, which is studied in detail.
Citation
Norman R. Draper. Berthold Heiligers. Friedrich Pukelsheim. "Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients." Ann. Statist. 28 (2) 578 - 590, April 2000. https://doi.org/10.1214/aos/1016218231
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