# Improvements on removing non-optimal support points in D-optimum design algorithms

Abstract : We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a $D$-optimum design. 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, and how it can be used to accelerate algorithms for $D$-optimum design.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00158649
Contributor : Luc Pronzato <>
Submitted on : Friday, June 29, 2007 - 11:14:19 AM
Last modification on : Monday, March 18, 2019 - 6:36:51 PM
Document(s) archivé(s) le : Thursday, April 8, 2010 - 7:34:30 PM

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SPL-HarmanP-revised2-2006.pdf
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### Identifiers

• HAL Id : hal-00158649, version 1
• ARXIV : 0706.4394

### Citation

Radoslav Harman, Luc Pronzato. Improvements on removing non-optimal support points in D-optimum design algorithms. Statistics and Probability Letters, Elsevier, 2007, 77, pp.90-94. ⟨hal-00158649⟩

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