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* Corresponding author 1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 LSTA - Laboratoire de Statistique Théorique et Appliquée 3 DMA - Département de Mathématiques et Applications 4 CLASSIC - Computational Learning, Aggregation, Supervised Statistical, Inference, and Classification DMA - Département de Mathématiques et Applications, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt 5 SOCS - School of Computer Science Quebec 6 SCS - School of computer science Ottawa 7 CSE - Department of Computer Science and Software Engineering Montreal

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.

Keywords : Nonparametric estimation Regression function estimation Affine invariance Nearest neighbor methods Mathematical statistics





Autor: Gérard Biau - Luc Devroye - Vida Dujmovic - Adam Krzyzak -

Fuente: https://hal.archives-ouvertes.fr/



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