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

Mathematica Slovaca

Radoslav Harman¹  Mária Trnovská¹ 

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

DOI  :  10.2478/s12175-009-0157-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In the paper we solve the problem of D â„‹-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 â„‹-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D â„‹-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D â„‹-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.

【 授权许可】

Unknown