A weighted k-nearest neighbor density estimate for geometric inference - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Statistics Year : 2011

A weighted k-nearest neighbor density estimate for geometric inference

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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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Dates and versions

hal-01094871 , version 1 (14-12-2014)

Identifiers

  • HAL Id : hal-01094871 , version 1

Cite

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 , 2011, 5, pp.204-237. ⟨hal-01094871⟩
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