Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence - Fabian Dunker (Georg-August-Universität Göttingen, Courant Research Centre - Poverty, Equity and Growth (CRC-PEG), 2015)
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.
Keywords: C13; C14; C31; C36; 330; nonparametric regression; instrumental variables; nonlinear inverse problems; iterative regularization