Before revision:  The new estimator is an adaptation of a nearest-neighbours estimator of a conditional mean (Yang, 1981; Stute, 1984), and is under mild conditions consistent and asymptotically normal with a rate of convergence that is the same regardless of the degree to which selection depends on unobservables in the outcome equation .
After revision:  The new estimator , unlike other proposals in the literature, is under mild conditions consistent and asymptotically normal with a rate of convergence that is the same regardless of the degree to which selection depends on unobservables in the outcome equation .