We study a wide class of nonparametric regression function estimators including kernel estimators and robust smoothers. Under different assumptions on the kernel and the sequence of bandwidths, we obtain weak uniform consistency rates on a bounded interval. The uniform consistency is shown in a "stochastic design model" and in a "fixed design model".
"Uniform Consistency of a Class of Regression Function Estimators." Ann. Statist. 12 (2) 612 - 623, June, 1984. https://doi.org/10.1214/aos/1176346509