Local convex hull support and boundary estimation

In this paper we introduce a new estimator for the support of a multivariate density. It is defined as a union of convex hulls of observations contained in balls of fixed radius. We study the asymptotic behavior of this “local convex hull” for the estimation of the support and its boundary. When the support is smooth enough, the proposed estimator is proved to be, eventually almost surely, homeomorphic to the support. Numerical simulations on simulated data illustrate the performance of our estimator.