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

Journal of Econometrics, 2014, vol. 178, issue P3, 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.

Keywords: Nonparametric regression; Nonlinear inverse problems; Iterative regularization; Instrumental regression (search for similar items in EconPapers)
JEL-codes: C13 C14 C30 C31 C36 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (32)

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Related works:
Working Paper: Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression (2014)
Working Paper: Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression (2013)
Working Paper: Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:178:y:2014:i:p3:p:444-455

DOI: 10.1016/j.jeconom.2013.06.001

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