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December 2005 Nonparametric methods for inference in the presence of instrumental variables
Peter Hall, Joel L. Horowitz
Ann. Statist. 33(6): 2904-2929 (December 2005). DOI: 10.1214/009053605000000714

Abstract

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the “difficulty” of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.

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Peter Hall. Joel L. Horowitz. "Nonparametric methods for inference in the presence of instrumental variables." Ann. Statist. 33 (6) 2904 - 2929, December 2005. https://doi.org/10.1214/009053605000000714

Information

Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62033
MathSciNet: MR2253107
Digital Object Identifier: 10.1214/009053605000000714

Subjects:
Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • December 2005
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