Adaptive wavelet estimation of a function in an indirect regression model

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We consider a nonparametric regression model where $m$ noise-perturbed functions $f_1,\ldots,f_m$ are randomly observed. For a fixed $\nu\in \{1,\ldots,m\}$, we want to estimate $f_{\nu}$ from the observations. To reach this goal, we develop an adaptive wavelet estimator based on a hard thresholding rule. Adopting the minimax approach under the mean integrated squared error over Besov balls, we prove that it attains a sharp rate of convergence.

Mots clés: Indirect nonparametric regression; Minimax estimation; Besov balls; Wavelets; Hard thresholding

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

Christophe Chesneau. Adaptive wavelet estimation of a function in an indirect regression model. 2010. ⟨hal-00497343⟩