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December 1997 A plug-in approach to support estimation
Antonio Cuevas, Ricardo Fraiman
Ann. Statist. 25(6): 2300-2312 (December 1997). DOI: 10.1214/aos/1030741073


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.


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Antonio Cuevas. Ricardo Fraiman. "A plug-in approach to support estimation." Ann. Statist. 25 (6) 2300 - 2312, December 1997.


Published: December 1997
First available in Project Euclid: 30 August 2002

zbMATH: 0897.62034
MathSciNet: MR1604449
Digital Object Identifier: 10.1214/aos/1030741073

Primary: 62G07
Secondary: 62G20

Keywords: $L_1$-approach , Hausdorff metric , kernel density estimators , multivariate spacings , support estimation

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 6 • December 1997
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