BHATIA, R.: Matrix Analysis. Grad. Texts in Math. 169, Springer-Verlag, New York, 1996.
 HARMAN, R. PRONZATO, L.: Improvements on removing nonoptimal support points in D-optimum design algorithms, Statist. Probab. Lett. 77, (2007), 90–94. http://dx.doi.org/10.1016/j.spl.2006.05.014 [Web of Science] [CrossRef]
 KIEFER, J. WOLFOWITZ, J.: The equivalence of two extremum problems, Canad. J. Math. 12, (1960), 363–366.
 PÁZMAN, A.: Foundations of Optimum Experimental Design, Reidel, Dordrecht, 1986.
 PUKELSHEIM, F.: Optimal Design of Experiments, John Wiley & Sons, New York, 1993.
 TITTERINGTON, D.: Algorithms for computing D-optimal designs on a finite design space. In: Proceedings of the 1976 Conference on Information Science and Systems. Department of Electronic Engineering, John Hopkins University, Baltimore, 1976, pp. 213–216.
 TORSNEY, B.: A moment inequality and monotonicity of an algorithm. In: Proceedings of the International Symposium on Semi-Infinite Programming and Applications (K. Kortanek, A. Fiacco, eds.), Springer-Verlag, Heidelberg, 1983, pp. 249–260.
 ZHANG, F.: Matrix Theory, Springer-Verlag, New York, 1999.
Editor-in-Chief: Pulmannová, Sylvia
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Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices
© 2009 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)
Citation Information: Mathematica Slovaca. Volume 59, Issue 6, Pages 693–704, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: 10.2478/s12175-009-0157-9, November 2009
- Published Online:
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.
MSC: Primary 62K05
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