Wavelet-based density estimation in a heteroscedastic convolution model

Christophe Chesneau (1) , Jalal M. Fadili (2)

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

We consider a heteroscedastic convolution density model under the "ordinary smooth case". We introduce a new adaptive wavelet estimator based on thresholding of estimated wavelet coefficients. Its asymptotic properties are explored via the minimax approach under the mean integrated squared error over Besov balls. We prove that our estimator attains near optimal rates of convergence (lower bounds are determined). Simulation results are reported to support our theoretical findings.

Mots clés: Density deconvolution; Heteroscedasticity; Rates of convergence; Wavelet bases; Hard thresholding; Lower bounds

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement des images [eess.IV]

Christophe Chesneau, Jalal M. Fadili. Wavelet-based density estimation in a heteroscedastic convolution model. Communications in Statistics - Theory and Methods, 2011, 42 (17), pp.3085-3099. ⟨10.1080/03610926.2011.615440⟩. ⟨hal-00565591v3⟩