Data-driven kNN estimation in nonparametric functional data analysis

JOURNAL OF MULTIVARIATE ANALYSIS

卷:153

Article

Kara, Lydia-Zaitri¹  Laksaci, Ali¹  Rachdi, Mustapha²  Vieu, Philippe³ 

[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

关键词: Functional data analysis;    UINN consistency;    Functional nonparametric statistics;    kNN estimator;    Data-driven estimator;   

DOI  :  10.1016/j.jmva.2016.09.016

来源: Elsevier

【 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.

【 授权许可】

Free