A plug-in approach to support estimation

Abstract

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.