Weak and strong uniform consistency of kernel regression estimates

Summary We study the estimation of a regression function by the kernel method. Under mild conditions on the window, the bandwidth and the underlying distribution of the bivariate observations {(X_i, Y_i)}, we obtain the weak and strong uniform convergence rates on a bounded interval. These results parallel those of Silverman (1978) on density estimation and extend those of Schuster and Yakowitz (1979) and Collomb (1979) on regression estimation.This research was carried out in part while the authors were guests at the University of Heidelberg, Germany, under the sponsorship of the Sonderforschungsbereich 123 in the summer of 1980