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An affine invariant k-nearest neighbor regression estimate

Gérard Biau, Luc Devroye, Vida Dujmović and Adam Krzyżak

Journal of Multivariate Analysis, 2012, vol. 112, issue C, 24-34

Abstract: 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.

Keywords: Nonparametric estimation; Regression function estimation; Affine invariance; Nearest neighbor methods; Mathematical statistics (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2012.05.020

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