D-Optimal Axial Designs for Quadratic and Cubic Additive Mixture Models |
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Authors: | L.Y. Chan,J.H. Meng,Y.C. Jiang,& Y.N. Guan |
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Affiliation: | The University of Hong Kong,;Northeastern University |
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Abstract: | The paper discusses D-optimal axial designs for the additive quadratic and cubic mixture models σ1≤i≤q(βixi + βiix2i) and σ1≤i≤q(βixi + βiix2i + βiiix3i), where xi≥ 0, x1 + . . . + xq = 1. For the quadratic model, a saturated symmetric axial design is used, in which support points are of the form (x1, . . . , xq) = [1 ? (q?1)δi, δi, . . . , δi], where i = 1, 2 and 0 ≤δ2 <δ1 ≤ 1/(q ?1). It is proved that when 3 ≤q≤ 6, the above design is D-optimal if δ2 = 0 and δ1 = 1/(q?1), and when q≥ 7 it is D-optimal if δ2 = 0 and δ1 = [5q?1 ? (9q2?10q + 1)1/2]/(4q2). Similar results exist for the cubic model, with support points of the form (x1, . . . , xq) = [1 ? (q?1)δi, δi, . . . , δi], where i = 1, 2, 3 and 0 = δ3 <δ2 < δ1 ≤1/(q?1). The saturated D-optimal axial design and D-optimal design for the quadratic model are compared in terms of their efficiency and uniformity. |
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Keywords: | additive mixture model D-optimality axial design uniformity of designs |
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