%0 Journal Article
%T Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression
%A Fabian Dunker
%A Jean-Pierre Florens
%A Thorsten Hohage
%A Jan Johannes
%A Enno Mammen
%J Statistics
%D 2013
%I arXiv
%R 10.1016/j.jeconom.2013.06.001
%X 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.
%U http://arxiv.org/abs/1307.6701v1