An affine invariant k-nearest neighbor regression estimate

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 conditions on k, and minimal requirements on the input data.

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Year of publication:	2012
Authors:	Biau, Gérard ; Devroye, Luc ; Dujmović, Vida ; Krzyżak, Adam
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 112.2012, C, p. 24-34
Publisher:	Elsevier
Subject:	Nonparametric estimation \| Regression function estimation \| Affine invariance \| Nearest neighbor methods \| Mathematical statistics

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011041952