K-Nearest Neighbour method in functional nonparametric regression

Abstract

The aim of this article is to study the k-nearest neighbour (kNN) method in nonparametric functional regression. We present asymptotic properties of the kNN kernel estimator: the almost-complete convergence and its rate. Then, we illustrate the effectiveness of this method by comparing it with the traditional kernel approach first on simulated datasets and then on a real chemometrical example. We also present in this article an important technical tool which could be useful in many other situations than ours.