Abstract
This 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 \(q = 3, 4.\)
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Sinha, B.K., Mandal, N.K., Pal, M., Das, P. (2014). Optimal Designs for Estimation of Optimum Mixture in Scheffé’s Quadratic Model. In: Optimal Mixture Experiments. Lecture Notes in Statistics, vol 1028. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1786-2_7
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DOI: https://doi.org/10.1007/978-81-322-1786-2_7
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