An affine invariant k-nearest neighbor regression estimate

JOURNAL OF MULTIVARIATE ANALYSIS

卷:112

Article

Biau, Gerard^1,2,3  Devroye, Luc⁴  Dujmovic, Vida⁵  Krzyzak, Adam⁶ 

[1] Univ Paris 06, LSTA, F-75252 Paris 05, France

[2] Univ Paris 06, LPMA, F-75252 Paris 05, France

[3] Ecole Normale Super, DMA, F-75230 Paris 05, France

[4] McGill Univ, Sch Comp Sci, Montreal, PQ H3A 2K6, Canada

[5] Carleton Univ, Sch Comp Sci, Herzberg Labs 5302, Ottawa, ON K1S 5B6, Canada

[6] Concordia Univ, Dept Comp Sci & Software Engn, Montreal, PQ H3G 1M8, Canada

关键词: Nonparametric estimation;    Regression function estimation;    Affine invariance;    Nearest neighbor methods;    Mathematical statistics;   

DOI  :  10.1016/j.jmva.2012.05.020

来源: Elsevier

【 摘 要 】

We design a data-dependent metric in lie and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on k, and minimal requirements on the input data. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free