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

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dc.creatorHarman, Radoslav
dc.creatorPronzato, Luc
dc.date2007-06-29
dc.date.accessioned2026-07-07T08:13:07Z
dc.date.available2026-07-07T08:13:07Z
dc.descriptionWe 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 $ξ$ be any design on a compact space $\mathcal{X} \subset \mathbb{R}^m$ with a nonsingular information matrix, and let $m+ε$ be the maximum of the variance function $d(ξ,\mathbf{x})$ 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 $d(ξ,\mathbf{x}_{*}) \geq m(1+ε/2-\sqrt{ε(4+ε-4/m)}/2)$. We show that this new lower bound on $d(ξ,\mathbf{x}_{*})$ is, in a sense, the best possible, and how it can be used to accelerate algorithms for $D$-optimum design.
dc.description5 pages Statistics and Probability letters available online at: http://www.elsevier.com/locate/stapro
dc.identifierhttps://arxiv.org/abs/0706.4394
dc.identifierhttp://arxiv.org/abs/0706.4394
dc.identifierStatistics & Probability Letters / Statistics and probability Letters 77 (2007) 90-94
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132691
dc.subjectStatistics Theory
dc.subject62K05, 90C46
dc.titleImprovements on removing non-optimal support points in D-optimum design algorithms
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