Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition
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Title: | Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition |
Author: | Arias Castro, Ery Pateiro López, Beatriz Rodríguez Casal, Alberto |
Affiliation: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
Subject: | Minimax lower bound | r-convex hull | Rolling condition | Support estimation | Volume estimation | |
Date of Issue: | 2018 |
Publisher: | Taylor & Francis |
Citation: | Arias-Castro, E., Pateiro-López, B., & Rodríguez-Casal, A. (2018). Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition. Journal Of The American Statistical Association, 1-12. doi: 10.1080/01621459.2018.1482751 |
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 |
Description: | This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 2018, available online: http://www.tandfonline.com/10.1080/01621459.2018.1482751 |
Publisher version: | https://doi.org/10.1080/01621459.2018.1482751 |
URI: | http://hdl.handle.net/10347/18629 |
DOI: | 10.1080/01621459.2018.1482751 |
ISSN: | 0162-1459 |
E-ISSN: | 1537-274X |
Rights: | © 2018 American Statistical Association |
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