# An Affine Invariant $k$-Nearest Neighbor Regression Estimate

* Corresponding author
4 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification
DMA - Département de Mathématiques et Applications - ENS Paris, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt
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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Cited literature [38 references]

https://hal.archives-ouvertes.fr/hal-00655850
Contributor : Gérard Biau <>
Submitted on : Wednesday, May 16, 2012 - 11:32:58 PM
Last modification on : Tuesday, May 14, 2019 - 11:02:08 AM
Long-term archiving on : Friday, August 17, 2012 - 2:40:48 AM

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• HAL Id : hal-00655850, version 2
• ARXIV : 1201.0586

### Citation

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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