Open Access
2011 A weighted k-nearest neighbor density estimate for geometric inference
Gérard Biau, Frédéric Chazal, David Cohen-Steiner, Luc Devroye, Carlos Rodríguez
Electron. J. Statist. 5: 204-237 (2011). DOI: 10.1214/11-EJS606


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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Gérard Biau. Frédéric Chazal. David Cohen-Steiner. Luc Devroye. Carlos Rodríguez. "A weighted k-nearest neighbor density estimate for geometric inference." Electron. J. Statist. 5 204 - 237, 2011.


Published: 2011
First available in Project Euclid: 14 April 2011

zbMATH: 1274.62264
MathSciNet: MR2792552
Digital Object Identifier: 10.1214/11-EJS606

Primary: 62G05 , 62G07
Secondary: 62G20

Keywords: central limit theorem , consistency , Density estimation , Geometric inference , k-nearest neighbor estimate , Level sets , rates of convergence , strong approximation , weighted estimate

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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