A weighted k-nearest neighbor density estimate for geometric inference

Gérard Biau; Frédéric Chazal; David Cohen-Steiner; Luc Devroye; Carlos Rodríguez

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

Document type :

Journal articles

Domain :

Statistics [stat]

Computer Science [cs] / Computational Geometry [cs.CG]

Complete list of metadatas

https://hal.inria.fr/hal-01094871
Contributor : Frédéric Chazal <>
Submitted on : Sunday, December 14, 2014 - 11:33:16 AM
Last modification on : Tuesday, August 13, 2019 - 11:32:01 AM

A weighted k-nearest neighbor density estimate for geometric inference

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A weighted k-nearest neighbor density estimate for geometric inference

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