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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


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.


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

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

Primary: 62G08
Secondary: 62G20

Keywords: bandwidth , convergence rate , eigenvalue , endogenous variable , exogenous variable , kernel method , linear operator , Nonparametric regression , optimality , smoothing

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • December 2005
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