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

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.

References in corpus (3)

• Kernel density estimation via diffusion
• Nonparametric methods for inference in the presence of instrumental variables
• On rate optimal local estimation in nonparametric instrumental regression

Cited by in corpus (6)

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• Specification Testing in Nonparametric Instrumental Quantile Regression
• Identifiability of Sparse Causal Effects using Instrumental Variables
• Nonparametric Identification and Estimation with Independent, Discrete Instruments
• Nonclassical Measurement Error in the Outcome Variable