Fast nonparametric estimation for convolutions of densities

Christophe Chesneau (1) , Fabienne Comte (2) , Fabien Navarro (3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen

The present paper is concerned with the problem of estimating the convolution of densities. We propose an adaptive estimator based on kernel methods, Fourier analysis and the Lepski method. We study its $\mathbb{L}_2$-risk properties. Fast and new rates of convergence are determined for a wide class of unknown functions. Numerical illustrations, on both simulated and real data, are provided to assess the performances of our estimator.

Mots clés: Convolution of densities. Kernel estimation. Minimax rate. Nonparametric estimation; Convolution of densities. Kernel estimation. Minimax rate. Nonparametric estimation.

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

Christophe Chesneau, Fabienne Comte, Fabien Navarro. Fast nonparametric estimation for convolutions of densities. 2013. ⟨hal-00798766v1⟩