 |
|
|
|
| HAL : hal-00399604, version 1 |
| Fiche détaillée |  Récupérer au format |
|
|
|
|
| Wavelet estimation of the derivatives of an unknown function from a convolution model |
|
|
| Christophe Chesneau 1 |
|
|
| (26/06/2009) |
|
|
|
| We observe a stochastic process where a convolution product of an unknown function $f$ and a known function $g$ is corrupted by Gaussian noise. We wish to estimate the $d$-th derivatives of $f$ from the observations. To reach this goal, we develop an adaptive estimator based on wavelet block thresholding. We prove that it achieves near optimal rates of convergence under the mean integrated squared error (MISE) over a wide range of smoothness classes. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de Mathématiques Nicolas Oresme (LMNO) |
|
|
|
CNRS : UMR6139 – Université de Caen |
|
|
|
|
|
|
|
|
|
| LMNO |
|
|
|
|
| Domaine | : | Mathématiques/Statistiques |
|
|
| Deconvolution – Derivatives function estimation – Wavelets – Block thresholding |
|
|
|
| Liste des fichiers attachés à ce document : | |||||
|
|||||
|
|
|
| hal-00399604, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00399604 | |
| oai:hal.archives-ouvertes.fr:hal-00399604 | |
| Contributeur : Christophe Chesneau | |
| Soumis le : Vendredi 26 Juin 2009, 21:31:02 | |
| Dernière modification le : Samedi 27 Juin 2009, 08:00:24 | |
