02-04
A note on optimal mixture and mixture amount designs
by Heiligers, B.; Hilgers, R.-D.
Preprint series: 02-04, Preprints
The paper is published: Statistica Sinica 13 (2003), 3, S.709-726.
- MSC:
- 62K05 Optimal designs
- 62J05 Linear regression
Abstract: In many applications of mixture experiments in medicine or biology, for example, not only the proportions of the involved mixture ingredients, but also their total amount is of particular interest. This calls for disigns in mixture amount models, which are obtained from classical mixture setups by including terms capturing the total amount, simultaneously dropping the sidecondition on the proportions to sum up to one. While design optimality usually depends sensitively on the underlying model, we establish here a close relation between admissible mixture, and admissible mixture amount designs in additive and homogeneous models. This particularly allows to obtain D-, A- and V-optimal mixture amount from optimal mixture designs, and vice versa. We present some examples in Becker\'s and Scheff\xe9\'s mixture models.
Keywords: Admissibility, A-optimality, approximate design, Becker models, complete class, D-optimality, I-optimality, mixture amount experiments, mixture experiments, V-optimality, tic-type polynomials.
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