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

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

Document Type: Article
Year of publication: 2014
The title of a journal, publication series: Journal of Econometrics
Volume: 178
Issue number: 3
Page range: 444-455
Place of publication: Amsterdam [u.a.]
Publishing house: Elsevier
ISSN: 0304-4076
Publication language: English
Institution: Außerfakultäre Einrichtungen > SFB 884
Subject: 330 Economics
Keywords (English): Nonparametric regression ; Nonlinear inverse problems ; Iterative regularization ; 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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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