Kiefer-complete classes of designs for cubic mixture models. (English) Zbl 1196.62107
Viana, Marlos A. G. (ed.) et al., Algebraic methods in statistics and probability II. AMS special session algebraic methods in statistics and probability, March 27–29, 2009, University of Illinois at Urbana-Champaign, Champaign, Il, USA. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4891-3/pbk). Contemporary Mathematics 516, 1-17 (2010).
Summary: We consider a cubic regression model for mixture experiments and discuss the improvement of designs in terms of increasing symmetry (Kiefer ordering) as well as obtaining a larger moment matrix under the standard Loewner ordering. The key problem is the characterization of Loewner comparability of invariant moment matrices. This problem is solved using concepts from representation theory. Our investigation yields two results on complete classes of designs relative to the Kiefer ordering.
For the entire collection see [Zbl 1192.60005].
For the entire collection see [Zbl 1192.60005].
MSC:
| 62K99 | Design of statistical experiments |
| 20C30 | Representations of finite symmetric groups |
| 60E15 | Inequalities; stochastic orderings |
