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Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression. (English) Zbl 1293.62090

Summary: This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data.

MSC:

62G08 Nonparametric regression and quantile regression
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