On a Plug-In Wavelet Estimator for Convolutions of Densities

Christophe Chesneau (1) , Fabien Navarro (1, 2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Equipe Image - Laboratoire GREYC - UMR6072

The nonparametric estimation of the m-fold convolution power of an unknown function f is considered. We introduce an estimator based on a plug-in approach and a wavelet hard thresholding estimator. We explore its theoretical asymptotic performances via the mean integrated squared error assuming that f has a certain degree of smoothness. Applications and numerical examples are given for the standard density estimation problem and the deconvolution density estimation problem.

Mots clés: Hard thresholding; Rates of convergence; Convolutions estimation; Plug-in estimator; Wavelets

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

Christophe Chesneau, Fabien Navarro. On a Plug-In Wavelet Estimator for Convolutions of Densities. Journal of Statistical Theory and Practice, 2014, 8 (4), ⟨10.1080/15598608.2013.824824⟩. ⟨hal-00625912v2⟩