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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 regressionE(Y|X = x)is weakly or strongly consistent for almost allx(mu), wheremuis the probability measure ofX. The result is valid for any distribution ofX. 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 )