An affine invariant k-nearest neighbor regression estimate

被引：23

作者：

Biau, Gerard ^{[1
,2
,3
]}

Devroye, Luc ^{[4
]}

Dujmovic, Vida ^{[5
]}

Krzyzak, Adam ^{[6
]}

机构：

[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

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2012年 / 112卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Nonparametric estimation; Regression function estimation; Affine invariance; Nearest neighbor methods; Mathematical statistics; MULTIVARIATE SIGN; RANK-TESTS; LOCATION;

D O I：

10.1016/j.jmva.2012.05.020

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：24 / 34

页数：11

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