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On convergence of local averaging regression function estimates for the regularization of inverse problems

In this paper, we combine the ideas of regression function estimation on the one hand and regularization by discretization on the other hand to a regularization method for linear ill-posed problems with additive stochastic noise. A general convergence result is provided and its assumptions are verified for the partitioning estimators and to some extent for kernel estimators. As a class of examples of inverse problems, we consider Volterra integral equations of the first kind.