Adaptive wavelet estimator for nonparametric density deconvolution

The problem of estimating a density g based on a sample X₁, X₂,, Xₙ from $p = q*g$ is considered. Linear and nonlinear wavelet estimators based on Meyer-type wavelets are constructed. The estimators are asymptotically optimal and adaptive if g belongs to the Sobolev space Hα . Moreover, the estimators considered in this paper adjust automatically to the situation when g is supersmooth.