Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients
Norman R. Draper, Berthold Heiligers, Friedrich Pukelsheim
The Annals of Statistics · 2000 · Volume 28 · Issue 2
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.
Keywords
15A45, 15A69, 62J05, 62K99, Complete class results for the Kiefer design ordering, exchangeable designs, Kronecker model, Loewner matrix ordering,moment polytope, permutation invariant designs, Scheffé canonical polynomials, weighted centroid designs
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