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| HAL : hal-00748790, version 1 |
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| Comparison of kernel density estimators with assumption on number of modes |
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Raphaël Coudret 1, 2, 3Gilles Durrieu 4 |
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| (01/05/2012) |
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| A data-driven bandwidth choice for a kernel density estimator called critical bandwidth is investigated. This procedure allows the estimation to have as many modes as assumed for the density to estimate. Both Gaussian and uniform kernels are considered. For the Gaussian kernel, asymptotic results are given. For the uniform kernel, an argument against these properties is mentioned. These theoretical results are illustrated with a simulation study which compare the kernel estimators that rely on critical bandwidth with another one which uses a plug-in method to select its bandwidth. An estimator that consists in estimates of density contour clusters and takes assumptions on number of modes into account is also considered. Finally, the methodology is illustrated using environment monitoring data. |
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| 1 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 2 : | CQFD (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251 |
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| 3 : | Environnements et Paléoenvironnements OCéaniques (EPOC) |
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CNRS : UMR5805 – INSU – Université Sciences et Technologies - Bordeaux I – Ecole Pratique des Hautes Etudes – Observatoire Aquitain des Sciences de l'Univers |
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| 4 : | Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885 (LMAM) |
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Université de Bretagne Sud |
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| Equipe CQFD |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Bandwidth – kernel density estimator – mode – numerical study – valvometry |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00748790, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00748790 | |
| oai:hal.archives-ouvertes.fr:hal-00748790 | |
| Contributeur : Raphaël Coudret | |
| Soumis le : Mardi 6 Novembre 2012, 08:39:35 | |
| Dernière modification le : Mardi 6 Novembre 2012, 08:58:01 | |
