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April 2000 Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients
Norman R. Draper, Berthold Heiligers, Friedrich Pukelsheim
Ann. Statist. 28(2): 578-590 (April 2000). DOI: 10.1214/aos/1016218231


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.


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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.


Published: April 2000
First available in Project Euclid: 15 March 2002

zbMATH: 1105.62363
MathSciNet: MR1790010
Digital Object Identifier: 10.1214/aos/1016218231

Primary: 62J05 , 62K99
Secondary: 15A45 , 15A69

Keywords: 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

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 2 • April 2000
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