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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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:112:y:2012:i:c:p:24-34
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DOI: 10.1016/j.jmva.2012.05.020
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