Adaptive estimation in the functional nonparametric regression model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:146

Article

Chagny, Gaelle¹  Roche, Angelina² 

[1] Univ Rouen, LMRS, UMR CNRS 6085, F-76821 Mont St Aignan, France

[2] Univ Paris 05, MAP5, UMR CNRS 8145, Paris, France

关键词: Functional data analysis;    Regression estimation;    Nonparametric kernel estimators;    Bandwidth selection;   

DOI  :  10.1016/j.jmva.2015.07.001

来源: Elsevier

【 摘 要 】

In this paper, we consider nonparametric regression estimation when the predictor is a functional random variable (typically a curve) and the response is scalar. Starting from a classical collection of kernel estimates, the bias variance decomposition of a pointwise risk is investigated to understand what can be expected at best from adaptive estimation. We propose a fully data-driven local bandwidth selection rule in the spirit of the Goldenshluger and Lepski method. The main result is a nonasymptotic risk bound which shows the optimality of our tuned estimator from the oracle point of view. Convergence rates are also derived for regression functions belonging to Holder spaces and under various assumptions on the rate of decay of the small ball probability of the explanatory variable. A simulation study also illustrates the good practical performances of our estimator. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free