Penalized contrast estimator for adaptive density deconvolution

Abstract

Abstract The authors consider the problem of estimating the density g of independent and identically distributed variables X I , from a sample Z 1 ,… Z n such that Z I = X I + σϵ for i = 1,…, n, and E is noise independent of X, with σϵ having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.