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2002-04

A note on optimal mixture and mixture amount designs

by Heiligers, B., Hilgers, R.-D..


Series: 2002-04, Preprints

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 Scheffé'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.

This paper was published in:
Statistica Sinica 13 (2003), 3, S.709-726.