Fast nonparametric estimation for convolutions of densities.

Summary The present paper is concerned with the problem of estimating the convolution of densities. We propose an adaptive estimator based on kernel methods, Fourier analysis and the Lepski method. We study its $\mathbb{L}_2$-risk properties. Fast and new rates of convergence are determined for a wide class of unknown functions. Numerical illustrations, on both simulated and real data, are provided to assess the performances of our estimator.