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arXiv · 1309.6602

Adaptive estimation of convex and polytopal support

Victor-Emmanuel Brunel
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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 $d\geq 3$, 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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Victor-Emmanuel Brunel. 2013-09-25. Adaptive estimation of convex and polytopal support. https://arxiv.org/abs/1309.6602

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