Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression

Fabian Dunker, Jean-Pierre Florens, Thorsten Hohage, Jan Johannes, and Enno Mammen


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.


Ill-posed integral equation; Landweber iteration; IV quantile; Kernel smoothing;

JEL codes

  • C13: Estimation: General
  • C14: Semiparametric and Nonparametric Methods: General
  • C30: General
  • C31: Cross-Sectional Models • Spatial Models • Treatment Effect Models • Quantile Regressions • Social Interaction Models

See also

Published in

Journal of Econometrics, vol. 178, n. 3, January 2014, pp. 444–455