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.
https://hal.inria.fr/hal-01094871
Contributeur : Frédéric Chazal
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Soumis le : dimanche 14 décembre 2014 - 11:33:16
Dernière modification le : mardi 24 avril 2018 - 17:20:06
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. 〈http://projecteuclid.org/euclid.ejs/1302784854〉. 〈hal-01094871〉
