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| HAL : hal-00175395, version 3 |
| arXiv : 0709.4543 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (28-09-2007) | v2 (02-03-2008) | v3 (17-01-2009) |
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| Piecewise linear density estimation for sampled data |
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| François-Xavier Lejeune 1 |
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| (27/09/2007) |
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| Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency polygons can reach the same optimal $L_{2}$-rates as in the independent and identically distributed case. Moreover, thanks to a suitable ``high frequency'' sampling design, these rates are derived together with a minimized time of observation depending on the regularity of sample paths. |
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| 1 : | Laboratoire de Statistique Théorique et Appliquée (LSTA) |
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Université Paris VI - Pierre et Marie Curie |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| nonparametric density estimation – histogram – frequency polygon – sampling – mean integrated squared error – rate of convergence |
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| hal-00175395, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00175395 | |
| oai:hal.archives-ouvertes.fr:hal-00175395 | |
| Contributeur : François-Xavier Lejeune | |
| Soumis le : Vendredi 16 Janvier 2009, 23:40:59 | |
| Dernière modification le : Samedi 17 Janvier 2009, 08:20:46 | |
