Nonlinear estimation problems

The maximum likelihood or least squares estimators are solutions of (in general) nonlinear equations and those are very often ill-posed. Hence we consider in the first part the regularization of ill-posed problems and find that in linear cases an optimal regularization is to be found. In nonlinear problems an optimal regularization is unknown. In the second part we consider a nonparametric goodness of fit and find that the maximum likelihood estimator has an asymptotic expansion which is used for the computation of the power of the test.