Adaptive estimation for some nonparametric instrumental variable models with full independence

The problem of endogeneity in statistics and econometrics is often handled by introducing instrumental variables (IV) which fulfill the mean independence assumption, i.e. unobservable independent instruments. When full IV’s assumed, nonparametric IV regression models demand lead to nonlinear integral equations with unknown kernels. We prove convergence rates for integrated square error iteratively regularized Newton method applied these problems. Compared related results we derive stronger that rely on weaker nonlinearity restrictions. demonstrate numerical simulations a produces better than standard model.