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The Hilbert Kernel Regression Estimate

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Abstract

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that strong convergence cannot be obtained. This is particularly interesting as this regression estimate does not have a smoothing parameter.

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