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Affine invariance 1 Mathematical statistics 1 Nadaraya-Watson estimate 1 Nearest neighbor methods 1 Nonparametric estimation 1 Regression function estimation 1 bandwidth selection 1 convergence 1 kernel estimate 1 nonparametric estimation 1 regression function estimation 1
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Undetermined 2
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Article 2
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Devroye, Luc 2 Biau, Gérard 1 Dujmović, Vida 1 Györfi, Laszlo 1 Krzyzak, Adam 1 Krzyżak, Adam 1
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Journal of Multivariate Analysis 2
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RePEc 2
Showing 1 - 2 of 2
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An affine invariant k-nearest neighbor regression estimate
Biau, Gérard; Devroye, Luc; Dujmović, Vida; Krzyżak, Adam - In: Journal of Multivariate Analysis 112 (2012) C, pp. 24-34
We design a data-dependent metric in Rd and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual...
Persistent link: https://www.econbiz.de/10011041952
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The Hilbert Kernel Regression Estimate
Devroye, Luc; Györfi, Laszlo; Krzyzak, Adam - In: Journal of Multivariate Analysis 65 (1998) 2, pp. 209-227
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...
Persistent link: https://www.econbiz.de/10005106960
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