Weak and strong uniform consistency of kernel regression estimates

Abstract

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 {(Xi, Yi)}, 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. © 1982 Springer-Verlag.