Wavelet estimation of the derivatives of an unknown function from a convolution model

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Deconvolution; Derivatives function estimation; Wavelets; Block thresholding

Domaines: Statistiques [math.ST]

Christophe Chesneau. Wavelet estimation of the derivatives of an unknown function from a convolution model. 2009. ⟨hal-00399604⟩