Penalized contrast estimator for adaptive density deconvolution

The authors consider the problem of estimating the density g of independent and identically dis tributed variables Xi, from a sample Z1, ... , Z,, such that Zi = Xi + aei for i = 1, . ., n, and e is noise independent of X, with ae 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.

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