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| HAL : hal-00620965, version 2 |
| arXiv : 1109.1986 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (09-09-2011) | v2 (07-03-2012) |
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| Necessary and sufficient condition for the existence of a Fréchet mean on the circle |
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| Benjamin Charlier 1 |
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| (09/02/2012) |
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| Let $(\S^1,d_{\S^1})$ be the unit circle in $\R^2$ endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure $\mu$ to admit a well defined Fréchet mean on $(\S^1,d_{\S^1})$. %This criterion allows to recover already known sufficient conditions of existence. We derive a new sufficient condition of existence $P(\alpha,\varphi)$ with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it. |
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| 1 : | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219 |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| circular data – Fréchet mean – uniqueness |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00620965, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00620965 | |
| oai:hal.archives-ouvertes.fr:hal-00620965 | |
| Contributeur : Benjamin Charlier | |
| Soumis le : Mardi 6 Mars 2012, 15:53:43 | |
| Dernière modification le : Mercredi 7 Mars 2012, 08:40:56 | |
