PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Improvements on removing non-optimal support points in D-optimum design algorithms
Radoslav Harman and Luc Pronzato
Statistics and Probability Letters 2005.


We improve the inequality used in (Pronzato, 2003) to remove points from the design space during the search for a $D$-optimum design, which can be used to accelerate design algorithms. Let $\xi$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+\epsilon$ be the maximum of the variance function $d(\xi,\mathbf{x})$ over all $\mathbf{x} \in \mathcal{X}$. We prove that any support point $\mathbf{x}_{*}$ of a $D$-optimum design on $\mathcal{X}$ must satisfy the inequality $d(\xi,\mathbf{x}_{*}) \geq m(1+\epsilon/2-\sqrt{\epsilon(4+\epsilon-4/m)}/2)$. We show that this new lower bound on $d(\xi,\mathbf{x}_{*})$ is, in a sense, the best possible.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:1032
Deposited By:Luc Pronzato
Deposited On:22 July 2005