The focus of the paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions stemming from a structural econometric model: E [Y - f (Z) | W] = 0, and involving endogenous variables Y and Z and instruments W. The function f is the...

The focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model E[Y − f (Z) | W] = 0, and involve endogenous variables Y and Z and instruments W. The function f is the...

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...

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of √n– consistent estimators whose cardinality increases with sample size. A special case of our framework corresponds to the conditional moment restriction and the implied...