Minimax Estimation of the Volume of a Set with Smooth Boundary
Statistics Theory
2016-05-05 v1 Methodology
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1605.01333,
title = {Minimax Estimation of the Volume of a Set with Smooth Boundary},
author = {Ery Arias-Castro and Beatriz Pateiro-López and Alberto Rodríguez-Casal},
journal= {arXiv preprint arXiv:1605.01333},
year = {2016}
}