A weighted k-nearest neighbor density estimate for geometric inference
A weighted k-nearest neighbor density estimate for geometric inference
复制标题
DOI：
10.1214/11-ejs606
复制
发表时间：
2011-01-01
影响因子：
1.1
通讯作者：
Rodriguez, Carlos
中科院分区：
文献类型：
--
作者：
Biau, Gerard;Chazal, Frederic;Rodriguez, Carlos
出于广泛的潜在应用在拓扑和几何推理，我们介绍了加权版本的k-最近邻密度估计。建立了该估计的各种逐点相合性结果。我们在最轻的可能条件下提出了一个一般的中心极限定理。此外，得到了一个强逼近结果，并讨论了最佳权值集的选择。特别是，经典的k-最近邻估计在手稿中描述的意义上不是最优的。所提出的方法已被实施恢复水平集在模拟和现实生活中的数据。
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.