Wavelet estimation of the derivatives of an unknown function from a convolution model
Résumé
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.
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)
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