Nonlinear Inverse Problems with Noisy Operators

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The aim of this project is to study nonlinear ill-posed integral equations arising in nonparametric instrumental variables. We are particularly interested in the case that the error is independent of the instrument. The kernels of the integral operators are defined in terms of the joint densities of observable random variables and have to be estimated from the data. For the efficient solution of these nonlinear ill-posed operator equations with noisy operators we apply regularized Newton methods with appropriate stopping rules and study convergence properties of the final iterates.