摘要翻译:
我们改进了Pronzato[2003.去除D-最优设计算法中的非最优支撑点。statist.probab.lett.63,223-228]中的不等式,以便在寻找D$-最优设计时从设计空间中去除点。设$\xi$是紧空间$\mathcal{X}\子集\mathbb{R}^m$上具有非奇异信息矩阵的任意设计,并设$m+\epsilon$是在\mathcal{X}$中所有$\mathbf{X}上的方差函数$d(\xi,\mathbf{X})$的最大值。我们证明了$\mathcal{x}$上的$\mathbf{x}_{*}$的任何支撑点$\mathbf{x}_{*}$必须满足不等式$d(\xi,\mathbf{x}_{*})\geq m(1+\epsilon/2-\sqrt{\epsilon(4+\epsilon-4/m)}/2)$。我们证明了在$d(\xi,\mathbf{x}_{*})上的这个新的下界在某种意义上是最好的,以及如何利用它来加速$d$-最优设计的算法。
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英文标题:
《Improvements on removing non-optimal support points in D-optimum design
algorithms》
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作者:
Radoslav Harman, Luc Pronzato (I3S)
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
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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PDF链接:
https://arxiv.org/pdf/706.4394