Approximate $D$-optimal designs of experiments on the convex hull of a finite set of information matrices

Year, pages: 2009, 693 - 704

In the paper we solve the problem of $D_\mathcal{H}$-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 $D_\mathcal{H}$-optimality covers many special design settings, e.g., the $D$-optimal experimental design for multivariate regression models. For $D_\mathcal{H}$-optimal designs we prove several theorems generalizing known properties of standard $D$-optimality. Moreover, we show that $D_\mathcal{H}$-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.

Harman, R., Trnovská, M. 2009. Approximate $D$-optimal designs of experiments on the convex hull of a finite set of information matrices. In Mathematica Slovaca, vol. 59, no.6, pp. 693-704. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0157-9

Harman, R., Trnovská, M. (2009). Approximate $D$-optimal designs of experiments on the convex hull of a finite set of information matrices. Mathematica Slovaca, 59(6), 693-704. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0157-9