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Data-driven kNN estimation in nonparametric functional data analysis

Lydia-Zaitri Kara, Ali Laksaci, Mustapha Rachdi and Philippe Vieu

Journal of Multivariate Analysis, 2017, vol. 153, issue C, 176-188

Abstract: 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.

Keywords: Functional data analysis; UINN consistency; Functional nonparametric statistics; kNN estimator; Data-driven estimator (search for similar items in EconPapers)
Date: 2017
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