Optimal Designs for Estimation of Optimum Mixture in Scheffé’s Quadratic Model

Abstract

AbstractThis chapter examines the optimum designs for estimating the optimum mixing proportions in Scheffé’s quadratic mixture model with respect to the A-optimality criterion. By optimum mixing proportion, we refer to the one that maximizes the mean response. Since the dispersion matrix of the estimate depends on the unknown model parameters, a pseudo-Bayesian approach is used in defining the optimality criterion. The optimum designs under this criterion have been obtained for two- and three-component mixtures. Further, using Kiefer’s equivalence theorem, it has been shown that under invariant assumption on prior moments, the optimum design for a \(q\)-component mixture is a \((q, 2)\) simplex lattice design for \(q = 3, 4.\) KeywordsScheffé’s quadratic mixture modelEstimation of optimum mixing proportionsTrace criterionPseudo-Bayesian approachInvariance(\(q\), 2)-simplex lattice designKiefer’s equivalence theorem