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A weighted k-nearest neighbor density estimate for geometric inference

Gérard Biau 1, 2, 3 Frédéric Chazal 4 David Cohen-Steiner 4 Luc Devroye Carlos Rodríguez 5
1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LSTA - Laboratoire de Statistique Théorique et Appliquée
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
5 University at Albany [SUNY]
Abstract : Motivated by a broad range of potential applications in topological and geometric inference, we introduce a weighted version of the k-nearest neighbor density estimate. Various pointwise consistency results of this estimate are established. We present a general central limit theorem under the lightest possible conditions. In addition, a strong approximation result is obtained and the choice of the optimal set of weights is discussed. In particular, the classical k-nearest neighbor estimate is not optimal in a sense described in the manuscript. The proposed method has been implemented to recover level sets in both simulated and real-life data.
Keywords : geometric inference density estimation
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Journal articles
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https://hal.inria.fr/hal-01094871
Contributor : Frédéric Chazal <>
Submitted on : Sunday, December 14, 2014 - 11:33:16 AM
Last modification on : Monday, December 14, 2020 - 5:10:11 PM

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  • HAL Id : hal-01094871, version 1

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Citation

Gérard Biau, Frédéric Chazal, David Cohen-Steiner, Luc Devroye, Carlos Rodríguez. A weighted k-nearest neighbor density estimate for geometric inference. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2011, 5, pp.204-237. ⟨hal-01094871⟩

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