  In the framework of supervised classification (discrimination) for functional
data, it is shown that the optimal classification rule can be explicitly
obtained for a class of Gaussian processes with "triangular" covariance
functions. This explicit knowledge has two practical consequences. First, the
consistency of the well-known nearest neighbors classifier (which is not
guaranteed in the problems with functional data) is established for the
indicated class of processes. Second, and more important, parametric and
nonparametric plug-in classifiers can be obtained by estimating the unknown
elements in the optimal rule. The performance of these new plug-in classifiers
is checked, with positive results, through a simulation study and a real data
example.
