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arXiv · 1307.6701

Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression

Fabian Dunker·Jean-Pierre Florens·Thorsten Hohage·Jan Johannes·Enno Mammen
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Abstract

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.

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Fabian Dunker, Jean-Pierre Florens, Thorsten Hohage, Jan Johannes, Enno Mammen. 2013-07-25. Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression. https://doi.org/10.1016/j.jeconom.2013.06.001

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