A plug-in approach to support estimation
A plug-in approach to support estimation
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DOI：
10.1214/aos/1030741073
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发表时间：
1997-12
影响因子：
4.5
通讯作者：
A. Cuevas;R. Fraiman
中科院分区：
文献类型：
--
作者：
A. Cuevas;R. Fraiman
我们提出了一种新的方法，使用密度估计的基础上，估计（紧）支持的多元密度的问题。这个主题（由Grenander的模式分析激发）与检测和聚类有着有趣的联系。定义了一类基于密度的估计量。对于集合之间通常的基于测度的度量d μ，建立了这些估计量的一致性结果和收敛速度。进一步的收敛速度（关于d μ和Hausdorff度量d H）也得到了一些，相当直观的，形状的限制。
We suggest a new approach, based on the use of density estimators, for the problem of estimating the (compact) support of a multivariate density. This subject (motivated in terms of pattern analysis by Grenander) has interesting connections with detection and clustering. A natural class of density-based estimators is defined. Universal consistency results and convergence rates are established for these estimators, with respect to the usual measure-based metric d μ between sets. Further convergence rates (with respect to both d μ and the Hausdorff metric d H ) are also obtained under some, fairly intuitive, shape restrictions.