Deconvolution with unknown noise distribution

Abstract: « I consider the deconvolution problem in the case where no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on observations of the corrupted signal. I will prove the identifiability of the model up to translation when the signal has a Laplace transform with an exponential growth $rho$ smaller than 2 and when it can be decomposed into two dependent components, so that the identifiability theorem can be used for sequences of dependent data or for sequences of iid multidimensional data.  In the case of iid multidimensional  data, I will propose an adaptive estimator of the density of the signal and provide rates of convergence. This rate of convergence is known to be minimax when ρ = 1. «