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Distribution-free consistency of a nonparametric kernel regression estimate and classification

It is shown that the kernel estimate of the regression E(Y|X = x) is weakly or strongly consistent for almost all x(\mu) , where \mu is the probability measure of X . The result is valid for any distribution of X . The asymptotical optimality of classification rules derived from the estimate is examined. The optimality is independent of class distributions, i.e., it is distribution-free.