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A Weighted k-Nearest Neighbor Density Estimate for Geometric Inference

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.
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https://hal.inria.fr/inria-00560623
Contributor : Frédéric Chazal <>
Submitted on : Monday, March 28, 2011 - 9:05:17 PM
Last modification on : Friday, June 12, 2020 - 11:02:06 AM
Document(s) archivé(s) le : Sunday, December 4, 2016 - 12:17:35 AM

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  • HAL Id : inria-00560623, version 2

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Gérard Biau, Frédéric Chazal, David Cohen-Steiner, Luc Devroye, Carlos Rodriguez. A Weighted k-Nearest Neighbor Density Estimate for Geometric Inference. 2011. ⟨inria-00560623v2⟩

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