On a Plug-In Wavelet Estimator for Convolutions of Densities.

Summary The nonparametric estimation of the m-fold convolution power of an unknown function f is considered. We introduce an estimator based on a plug-in approach and a wavelet hard thresholding estimator. We explore its theoretical asymptotic performances via the mean integrated squared error assuming that f has a certain degree of smoothness. Applications and numerical examples are given for the standard density estimation problem and the deconvolution density estimation problem.