On estimating the perimeter using the alpha-shape
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| Title: | On estimating the perimeter using the alpha-shape |
| Author: | Arias Castro, Ery Rodríguez Casal, Alberto |
| Affiliation: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
| Subject: | Perimeter estimation | α-shape | r-convex hull | Rolling condition | Sets with positive reach | |
| Date of Issue: | 2017 |
| Publisher: | Institut Henri Poincaré |
| Citation: | Arias-Castro, Ery; Rodríguez-Casal, Alberto. On estimating the perimeter using the alpha-shape. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 3, 1051--1068. 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 |
| Publisher version: | https://doi.org/10.1214/16-AIHP747 |
| URI: | http://hdl.handle.net/10347/18623 |
| Rights: | © Association des Publications de l’Institut Henri Poincaré, 2017 |
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