Weak and strong uniform consistency of kernel regression estimates

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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.