This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator in statistics. We first establish a general upper bound...

This paper makes several contributions to the literature on the important yet difficult problem of estimating functions nonparametrically using instrumental variables. First, we derive the minimax optimal sup-norm convergence rates for nonparametric instrumental variables (NPIV) estimation of...

We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a kdimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we...

We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a k-dimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple definition, we...