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.
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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
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Mack, Y.P., Silverman, B.W. Weak and strong uniform consistency of kernel regression estimates. Z. Wahrscheinlichkeitstheorie verw. Gebiete 61, 405–415 (1982). https://doi.org/10.1007/BF00539840
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DOI: https://doi.org/10.1007/BF00539840