Asymptotic normality of a nonparametric instrumental variables estimator

This article gives conditions under which the nonparametric instrumental variables estimator of Hall and Horowitz (Annals of Statistics 33 (December 2005), 2904-2929) is asymptotically normally distributed. With sufficiently large samples, the asymptotic normality result can be used to form confidence intervals for the unknown function that is estimated by the Hall-Horowitz procedure. The article reports the results of a Monte Carlo investigation of the finite-sample coverage probabilities of the confidence intervals.