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Mathematica Slovaca

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

1Comenius University

© 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

Publication History

Published Online:
2009-11-11

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.

MSC: Primary 62K05

Keywords: D-optimal design; multivariate regression; multiplicative algorithm; D-optimal augmentation of trials

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