Nonparametric inference in convolution models

In this thesis, we deal with nonparametric inference for convolution models, which consider the density of the sum or product of real-valued random variables, that is, the additive or multiplicative convolution of the respective densities. Then, convolution theorems yield the multiplication of their corresponding Fourier transforms or Mellin transforms, respectively. These properties are exploited for nonparametric inference. In this thesis, we investigate two types of convolution models. Firstly, we estimate a function which is an image under convolutions. Secondly, we look at the estimation of a quadratic functional and hypothesis testing for an unknown density under multiplicative measurement errors.