Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence
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Date
2015
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Abstract
In econometrics some nonparametric instrumental regression models
and nonparametric demand models with endogeneity lead to nonlinear integral
equations with unknown integral kernels. We prove convergence rates of the
risk for the iteratively regularized Newton method applied to these problems.
Compared to related results we relay on a weaker non-linearity condition and
have stronger convergence results. We demonstrate by numerical simulations for
a nonparametric IV regression problem with continuous instrument and regressor
that the method produces better results than the standard method.
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Keywords
nonparametric regression, iterative regularization, nonlinear inverse problems, instrumental variables