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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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Contributor : Frédéric Chazal Connect in order to contact the contributor
Submitted on : Sunday, December 14, 2014 - 11:33:16 AM
Last modification on : Tuesday, January 25, 2022 - 1:02:03 PM


  • HAL Id : hal-01094871, version 1


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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