A-optimal designs for optimum mixture in an additive quadratic mixture model

ABSTRACT

In the analysis of experiments with mixtures, quadratic models have been widely used. The optimum designs for the estimation of optimum mixing proportions in a quadratic mixture model have been studied by Pal and Mandal [Optimum designs for optimum mixtures. Statist Probab Lett. 2006;76:1369–1379] and Mandal et al. [Optimum mixture designs: a pseudo-Bayesian approach. J Ind Soc Agric Stat. 2008;62(2):174–182; Optimum mixture designs under constraints on mixing components. Statist Appl. 2008;6(1&2) (New Series): 189–205], using a pseudo-Bayesian approach. In this paper, a similar approach has been employed to obtain the A-optimal designs for the estimation of optimum proportions in an additive quadratic mixture model, proposed by Darroch and Waller [Additivity and interaction in three-component experiments with mixture. Biometrika. 1985;72:153–163], when the number of components is 3, 4 and 5. It has been shown that the vertices of the simplex are necessarily the support points of the optimum design, and the other support points include barycentres of depth at most 2.

KEYWORDS:

• Mixture experiment
• Darroch–Waller model
• non-linear parametric function
• asymptotic efficiency
• A-optimal design

2010 AMS SUBJECT CLASSIFICATION:

• 62K99
• 62J05

Acknowledgments

The authors acknowledge with thanks the fruitful suggestions made by the anonymous Associate Editor and the referees, which immensely helped to improve the presentation of the paper. A part of the work was carried out when the first author was visiting the University of Memphis, USA. The first and the second authors also acknowledge the support for this work from their project under the UPE Scheme of Calcutta University.

Disclosure statement

No potential conflict of interest was reported by the authors.