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.
Publié le : 2000-04-15
Classification:
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,
62K99,
62J05,
15A69,
15A45
@article{1016218231,
author = {Draper, Norman R. and Heiligers, Berthold and Pukelsheim, Friedrich},
title = {Kiefer ordering of simplex designs for second-degree mixture
models with four or more ingredients},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 578-590},
language = {en},
url = {http://dml.mathdoc.fr/item/1016218231}
}
Draper, Norman R.; Heiligers, Berthold; Pukelsheim, Friedrich. Kiefer ordering of simplex designs for second-degree mixture
models with four or more ingredients. Ann. Statist., Tome 28 (2000) no. 3, pp. 578-590. http://gdmltest.u-ga.fr/item/1016218231/