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Reports (Research Report) Year : 2012

An Affine Invariant $k$-Nearest Neighbor Regression Estimate

Abstract

We design a data-dependent metric in $\mathbb R^d$ 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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Dates and versions

hal-00655850 , version 1 (02-01-2012)
hal-00655850 , version 2 (16-05-2012)

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Cite

Gérard Biau, Luc Devroye, Vida Dujmovic, Adam Krzyzak. An Affine Invariant $k$-Nearest Neighbor Regression Estimate. [Research Report] -. 2012. ⟨hal-00655850v2⟩
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