Deconvolution Problems in Nonparametric Statistics

This book gives an introduction to deconvolution problems in nonparametric statistics, e.g. density estimation based on contaminated data, errors-in-variables regression, and image reconstruction. Some real-life applications are discussed while we mainly focus on methodology (description of the estimation procedures) and theory (minimax convergence rates with rigorous proofs and adaptive smoothing parameter selection). In general, we have tried to present the proofs in such manner that only a low level of previous knowledge is needed. An appendix chapter on further results of Fourier analysis