Dunker, Fabian, Florens, Jean-Pierre, Hohage, Thorsten, Johannes, Jan and Mammen, Enno (2014) Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression. Journal of Econometrics, vol. 178 (n° 3). pp. 444-455.

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.