Statistica Sinica 19 (2009), 1055-1075

MODEL-ROBUST $D$- AND $A$-OPTIMAL DESIGNS

FOR MIXTURE EXPERIMENTS

Mong-Na Lo Huang$^1$, Hsiang-Ling Hsu$^1$, Chao-Jin Chou$^1$ and Thomas Klein$^2$

$^1$National Sun Yat-sen University and $^2$Technische Universität München

Abstract: This paper investigates optimal designs for mixture experiments when there is uncertainty as to whether a polynomial regression model of degree one or two is appropriate. Three groups of novel results are presented: (i) a complete class of designs relative to certain mixed design criteria, (ii) model-robust $D$- and $A$-optimal designs, (iii) $D$- and $A$-optimal designs with maximin efficiencies under variation of the design criterion.

Key words and phrases: centroid design, complete class, design efficiency, design optimality, exchangeability, Kiefer ordering, polynomial regression, robustness.