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| HAL : hal-00495449, version 2 |
| arXiv : 1006.5135 |
| DOI : 10.1016/j.spasta.2012.10.001 |
| Fiche détaillée |  Récupérer au format |
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| spatial statistics 2 (2012) 47-61 |
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| Versions disponibles : | v1 (26-06-2010) | v2 (28-06-2011) |
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| Level sets estimation and Vorob'ev expectation of random compact sets |
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Philippe Heinrich 1Radu Stoica 1 |
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| (12/2012) |
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| The issue of a ''mean shape'' of a random set $X$ often arises, in particular in image analysis and pattern detection. There is no canonical definition but one possible approach is the so-called Vorob'ev expectation $\E_V(X)$, which is closely linked to quantile sets. In this paper, we propose a consistent and ready to use estimator of $\E_V(X)$ built from independent copies of $X$ with spatial discretization. The control of discretization errors is handled with a mild regularity assumption on the boundary of $X$: a not too large 'box counting' dimension. Some examples are developed and an application to cosmological data is presented. |
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| 1 : | Laboratoire Paul Painlevé (LPP) |
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CNRS : UMR8524 – Université Lille I - Sciences et technologies |
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| 2 : | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP) |
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Polytechnique - X – CNRS : UMR7641 |
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| Domaine | : | Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie |
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| Stochastic geometry – Random closed sets – Level sets – Vorob'ev expectation |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00495449, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00495449 | |
| oai:hal.archives-ouvertes.fr:hal-00495449 | |
| Contributeur : Viet Chi Tran | |
| Soumis le : Lundi 27 Juin 2011, 16:06:15 | |
| Dernière modification le : Samedi 24 Novembre 2012, 19:29:16 | |
