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

arXiv: https://arxiv.org/abs/1307.6701 · HTML: https://mlsanity.com/paper/1307.6701/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2013.

## Built on by (most cited first, 3 of 3)

- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Identifiability of Sparse Causal Effects using Instrumental Variables](https://mlsanity.com/paper/2203.09380/) (2022)
- [Boosted Control Functions: Distribution generalization and invariance in confounded models](https://mlsanity.com/paper/2310.05805/) (2023)

## Abstract (arXiv)

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.