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

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2 Author(s)
Krzyzak, A. ; McGill University, Canada ; Pawlak, M.

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.

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Information Theory, IEEE Transactions on  (Volume:30 ,  Issue: 1 )