Stute, WinfriedKaiser, HenrikHenrikKaiser2023-05-022023-05-022023-04https://jlupub.ub.uni-giessen.de/handle/jlupub/16278http://dx.doi.org/10.22029/jlupub-15659In this thesis we study the additive model of errors in variables, which is also known as the deconvolution problem. The objective consists particularly in the reconstruction of the distribution F associated with a random variable X, which is observable only through a sample of a blurred variable Y, due to an additive random error ε with known distribution H. Our initial considerations yield an unbiased estimator for F for various discrete and some continuous distributions. A more general approach then leads us to the symmetrized model of errors in variables. It is obtained by an additional convolution of G with the conjugate error distribution of H, thereby resulting in an error distribution of symmetric type. As a consequence the characteristic function of X can be represented as the limit of a geometric series. By truncation of this series we deduce an approximation of F, which is valid for arbitrary error distributions. This approximation, termed the deconvolution function, converges to F in many cases. To determine the corresponding rates of convergence, techniques from complex calculus and particularly Mellin-Barnes integrals turn out to be appropriate. The latter describe a special class of integrals that can be evaluated by residue analysis. The results are established in a more general setting, which makes them applicable to other Laplace-type integrals. With the aid of the deconvolution function we also construct an estimator for F. The asymptotic properties of its variance, a peculiar integral of dimension two, can be specified by virtue of our findings from the concluding chapter. These results rely on iterated Mellin-Barnes integrals.enIn Copyrightdeconvolutionerrors in variablesmeasurement errorsprobabilitystochasticsasymptoticsLaplace-type integralsill-posed problemscomplex analysisspecial functionsresidue theoryFourier transformsMellin transformsMellin-Barnes integralsiterated integralsoperator theoryfunctional analysisddc:500ddc:510