A weighted k-nearest neighbor density estimate for geometric inference

作者：Biau Gerard^*; Chazal Frederic; Cohen Steiner David; Devroye Luc; Rodriguez Carlos

来源：Electronic Journal of Statistics, 2011, 5(none): 204-237.

DOI：10.1214/11-EJS606

• Geometric inference
• level sets
• density estimation
• k-nearest neighbor estimate
• weighted estimate
• consistency
• rates of convergence
• central limit theorem
• strong approximation

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.

• 出版日期2011
• 单位INRIA