Deconvolution of supersmooth densities with smooth noise

The author considers the estimation of the common probability density of independent and identically distributed random variables observed with added white noise. She assumes that the unknown density belongs to some class of supersmooth functions, and that the error distribution is ordinarily smooth, meaning that its characteristic function decays polynomially asymptotically. In this context, the author evaluates the minimax rate of convergence of the pointwise risk and describes a kernel estimator having this rate. She computes upper bounds for the double struk L sign₂ risk of this estimator.