A weighted k-nearest neighbor density estimate for geometric inference (original) (raw)
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
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.
Citation
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. https://doi.org/10.1214/11-EJS606
Information
Published: 2011
First available in Project Euclid: 14 April 2011
Digital Object Identifier: 10.1214/11-EJS606
Subjects:
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
Vol.5 • 2011
