Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices |
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Authors: | Radoslav Harman Mária Trnovská |
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Institution: | 1.Department of Applied Mathematics and Statistics Faculty of Mathematics, Physics and Informatics,Comenius University,Bratislava,Slovakia |
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Abstract: | In the paper we solve the problem of D
ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull
of a finite set of positive semidefinite matrices. The problem of D
ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D
ℋ-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D
ℋ-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We
illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane. |
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Keywords: | |
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