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August 2017 On estimating the perimeter using the alpha-shape
Ery Arias-Castro, Alberto Rodríguez-Casal
Ann. Inst. H. Poincaré Probab. Statist. 53(3): 1051-1068 (August 2017). DOI: 10.1214/16-AIHP747

Abstract

We consider the problem of estimating the perimeter of a smooth domain in the plane based on a sample from the uniform distribution over the domain. We study the performance of the estimator defined as the perimeter of the alpha-shape of the sample. Some numerical experiments corroborate our theoretical findings.

Nous considérons le problème de l’estimation du périmètre d’un domaine à bord lisse dans le plan basé sur un échantillon tiré de la loi uniforme ayant pour support le domaine en question. Nous étudions la performance de l’estimateur défini par le périmètre de la forme-alpha (« alpha-shape ») de l’échantillon. Des expériences numériques confirment notre théorie.

Citation

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Ery Arias-Castro. Alberto Rodríguez-Casal. "On estimating the perimeter using the alpha-shape." Ann. Inst. H. Poincaré Probab. Statist. 53 (3) 1051 - 1068, August 2017. https://doi.org/10.1214/16-AIHP747

Information

Received: 19 June 2015; Revised: 31 January 2016; Accepted: 13 February 2016; Published: August 2017
First available in Project Euclid: 21 July 2017

zbMATH: 06775431
MathSciNet: MR3689960
Digital Object Identifier: 10.1214/16-AIHP747

Subjects:
Primary: 60D05, 62G99

Rights: Copyright © 2017 Institut Henri Poincaré

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Vol.53 • No. 3 • August 2017
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