A plug-in approach to support estimation

• 成果类型: Article
• 署名作者: Cuevas, A; Fraiman, R
• 署名单位: Autonomous University of Madrid; Universidad de la Republica, Uruguay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 2300-2312
• 关键词: boundaries; Spacings; bounds

摘要

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(mu) between sets. Further convergence rates (with respect to both d(mu) and the Hausdorff metric d(H)) are also obtained under some, fairly intuitive, shape restrictions.