Wavelet density estimators for the deconvolution of a component from a mixture

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We consider the model: Y = X+e, where X and e are independent random variables. The density of e is known whereas the one of X is a finite mixture with unknown components. Considering the "ordinary smooth case" on the density of e, we want to estimate a component of this mixture. To reach this goal, we develop two wavelet estimators: a nonadaptive based on a projection and an adaptive based on a hard thresholding rule. We evaluate their performances by taking the minimax approach under the mean integrated squared error over Besov balls. We prove that the adaptive one attains a sharp rate of convergence.

Mots clés: Density deconvolution; Mixture; Minimax approach; Wavelets; Hard thresholding

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

Christophe Chesneau. Wavelet density estimators for the deconvolution of a component from a mixture. 2010. ⟨hal-00487347v2⟩