Kiefer ordering of simplex designs for second-degree mixture models with four or more ingredients

• 成果类型: Article
• 署名作者: Draper, NR; Heiligers, B; Pukelsheim, F
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Otto von Guericke University; University of Augsburg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016218231
• 发表日期: 2000
• 页码: 578-590
• 关键词: polynomial regression; Admissibility; optimality

摘要

For mixture models an 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.