Data-driven kNN estimation in nonparametric functional data analysis

被引：69

作者：

Kara, Lydia-Zaitri ^{[1
]}

Laksaci, Ali ^{[1
]}

Rachdi, Mustapha ^{[2
]}

Vieu, Philippe ^{[3
]}

机构：

[1] Univ Djillali Liabes Sidi Bel Abbes, LSPS, Sidi Bel Abbes, Algeria

[2] Univ Grenoble Alpes, AGIM Team, AGEIS EA 7407, Grenoble, France

[3] Univ Paul Sabatier, IMT, Toulouse, France

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2017年 / 153卷

关键词：

Functional data analysis; UINN consistency; Functional nonparametric statistics; kNN estimator; Data-driven estimator; UNIFORM CONSISTENCY; CONDITIONAL DENSITY; REGRESSION; CONVERGENCE;

D O I：

10.1016/j.jmva.2016.09.016

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：

Kernel nearest-neighbor (kNN) estimators are introduced for the nonparametric analysis of statistical samples involving functional data. Asymptotic theory is provided for several different target operators including regression, conditional density, conditional distribution and hazard operators. The main point of the paper is to consider data-driven methods of selecting the number of neighbors in order to make the proposed methods fully automatic. As a by-product of our proofs we state consistency results for kNN functional estimators which are uniform in the number of neighbors (UINN). Some simulated experiences illustrate the feasibility and the finite-sample behavior of the method. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：176 / 188

页数：13

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