Estimation of the derivatives of a function in a convolution regression model with random design

Christophe Chesneau (1) , Maher Kachour (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IDRAC Business school Lyon - Institut pour le Développement et la Recherche d'Action Commerciale

A convolution regression model with random design is considered. We investigate the estimation of the derivatives of an unknown function, element of the convolution product. We introduce new estimators based on wavelet methods and provide theoretical guaranties on their good performances.

Mots clés: Nonparametric regression; Deconvolution; Derivatives function estimation; wavelets

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

Christophe Chesneau, Maher Kachour. Estimation of the derivatives of a function in a convolution regression model with random design. 2015. ⟨hal-01054877v2⟩