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arXiv · 1605.01333

Minimax Estimation of the Volume of a Set with Smooth Boundary

Ery Arias-Castro·Beatriz Pateiro-López·Alberto Rodríguez-Casal
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Abstract

We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct the bias of the plug-in estimator based on the sample alpha-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings.

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Ery Arias-Castro, Beatriz Pateiro-López, Alberto Rodríguez-Casal. 2016-05-04. Minimax Estimation of the Volume of a Set with Smooth Boundary. https://arxiv.org/abs/1605.01333

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