Exact D-optimal designs for a linear log contrast model with mixture experiment for three and four ingredients |
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Authors: | Miao-Kuan Huang Mong-Na Lo Huang Baisuo Jin |
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Affiliation: | 1. Center for General Education, National Formosa University, Yunlin, Taiwan, ROC;2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, ROC;3. Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui, China |
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Abstract: | This study investigates the exact D-optimal designs of the linear log contrast model using the mixture experiment suggested by Aitchison and Bacon-Shone (1984) and the design space restricted by Lim (1987) and Chan (1988). Results show that for three ingredients, there are six extreme points that can be divided into two non-intersect sets S1 and S2. An exact N-point D -optimal design for N=3p+q,p≥1,1≤q≤2 arranges equal weight n/N,0≤n≤p at the points of S1 (S2) and puts the remaining weight (N−3n)/N on the points of S2 (S1) as evenly as possible. For four ingredients and N=6p+q,p≥1,1≤q≤5, an exact N-point design that distributes the weights as evenly as possible among the six supports of the approximate D-optimal design is exact D-optimal. |
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Keywords: | Approximate D-optimal design Extreme point Lagrange interpolation polynomial Geometric&ndash arithmetic means inequality |
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