Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence

摘要

In econometrics some nonparametric instrumental regression modelsand nonparametric demand models with endogeneity lead to nonlinear integralequations with unknown integral kernels. We prove convergence rates of therisk for the iteratively regularized Newton method applied to these problems.Compared to related results we relay on a weaker non-linearity condition andhave stronger convergence results. We demonstrate by numerical simulations fora nonparametric IV regression problem with continuous instrument and regressorthat the method produces better results than the standard method.