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Nonparametric instrumental regression with non-convex constraints

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Grasmair, Markus ; Scherzer, Otmar ; Vanhems, Anne:
Nonparametric instrumental regression with non-convex constraints.
In: Inverse Problems. Bd. 29 (2013) Heft 3.
ISSN 0266-5611 ; 1361-6420

Volltext

Link zum Volltext (externe URL): http://dx.doi.org/10.1088/0266-5611/29/3/035006

Kurzfassung/Abstract

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, such as integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition.

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Publikationsform:Artikel
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen/Informatik
Peer-Review-Journal:Ja
Titel an der KU entstanden:Ja
Eingestellt am:27. Feb 2013 10:13
Letzte Änderung:24. Mai 2016 11:19
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/12948/