Wavelet-based density estimation in a heteroscedastic convolution model

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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).

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

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

Christophe Chesneau. Wavelet-based density estimation in a heteroscedastic convolution model. 2011. ⟨hal-00565591v2⟩