A plug-in approach to support estimation

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