Adaptive estimation of convex and polytopal support

2013/09/25 by Victor-Emmanuel Brunel, Brunel, Victor-Emmanuel · 1 citation
Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1309.6602

arxiv created 2013/09/25 · openalex publication_date 2013/09/25 · arxiv updated 2013/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in \R^d. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension d, unlike the other estimators that have been proposed so far. For d≥ 3, our estimator has a better risk than the previous ones, and it is nearly minimax, up to a logarithmic factor. We also propose an estimator which is adaptive with respect to the structure of the boundary of the unknown support.

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