Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

Ery Arias-Castro, Beatriz Pateiro-López and Alberto Rodríguez-Casal

Journal of the American Statistical Association, 2019, vol. 114, issue 527, 1162-1173

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 that 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 α-convex hull. We show that this simple estimator achieves a minimax lower bound that we derive. Some numerical experiments corroborate our theoretical findings. Supplementary materials for this article are available online.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:114:y:2019:i:527:p:1162-1173

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DOI: 10.1080/01621459.2018.1482751

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