  The problem of supervised classification (or discrimination) with functional
data is considered, with a special interest on the popular k-nearest neighbors
(k-NN) classifier. First, relying on a recent result by Cerou and Guyader
(2006), we prove the consistency of the k-NN classifier for functional data
whose distribution belongs to a broad family of Gaussian processes with
triangular covariance functions. Second, on a more practical side, we check the
behavior of the k-NN method when compared with a few other functional
classifiers. This is carried out through a small simulation study and the
analysis of several real functional data sets. While no global "uniform" winner
emerges from such comparisons, the overall performance of the k-NN method,
together with its sound intuitive motivation and relative simplicity, suggests
that it could represent a reasonable benchmark for the classification problem
with functional data.
