Local Convex Hull support and boundary estimation
Résumé
We consider random samples in $\mathbb{R}^d$ drawn from an unknown density. This paper is devoted to presenting a new estimator of the support of the density, which is based on a local convexity criteria. We prove that the estimator is consistent and that it also provides a consistent estimator for the boundary. Some convergence rates are given depending on different asumptions and one can also prove that when the boundary is smooth enough and when the density go to $0$ as a power of the distance to the boundary the estimator is (eventually almost surely) homeomorph to the support.
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