Data-driven NN estimation in nonparametric functional data analysis

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• 作者：Lydia-Zaitri Kara^a ; ^{karazaitri@hotmail.fr} ; Ali Laksaci^a ; ^{alilak@yahoo.fr} ; Mustapha Rachdi^b ; ^{mustapha.rachdi@univ-grenoble-alpes.fr} ; Philippe Vieu^c ; ^{vieu@math.univ-toulouse.fr}
• 关键词：primary ; 62G05 ; 62G08 ; 62G20 ; 62G35 ; 62G07 ; 62G32 ; 62G30 ; secondary ; 62H12
• 刊名：Journal of Multivariate Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：153
• 期：Complete
• 页码：176-188
• 全文大小：644 K
• 卷排序：153

文摘

Kernel nearest-neighbor (kkNN) 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 kkNN 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.