Stone proved that nearest neighbor estimates of a nonparametric regression function are "universally" consistent. We show that the same holds for window estimates, and we obtain a rate of convergence under some restrictions.
"Consistent Window Estimation in Nonparametric Regression." Ann. Statist. 8 (2) 240 - 246, March, 1980. https://doi.org/10.1214/aos/1176344950