Adaptive wavelet estimator for a function and its derivatives in an indirect convolution model

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We consider an indirect convolution model where $m$ blurred and noise-perturbed functions $f_1,\ldots,f_m$ are randomly observed. For a fixed $\omega\in \{1,\ldots,m\}$, we want to estimate $f_{\omega}$ and its derivatives. An adaptive nonlinear wavelet estimator using a singular value decomposition is developed. Taking the mean integrated squared error over Besov balls, we prove that it attains a fast rate of convergence.

Mots clés: Deconvolution; Function estimation; Wavelets; Hard thresholding

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Chesneau. Adaptive wavelet estimator for a function and its derivatives in an indirect convolution model. 2012. ⟨hal-00508811v2⟩