On the mean integrated squared error of a plug-in estimator for convolutions

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

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen

The nonparametric estimation of convolutions is considered. Using the mean integrated squared error, we explore the performance of a plug-in estimator under mild assumptions on the model. We illustrate these general results via wavelet hard thresholding estimators for two different density estimation problems. In particular, we prove that they attain fast rates of convergence for a wide class of unknown functions. Simulation results illustrate the theory.

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

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

Christophe Chesneau, Fabien Navarro. On the mean integrated squared error of a plug-in estimator for convolutions. 2011. ⟨hal-00625912v1⟩