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In the framework of supervised classification (discrimination) for functionaldata, it is shown that the optimal classification rule can be explicitlyobtained for a class of Gaussian processes with "triangular" covariancefunctions. This explicit knowledge has two practical consequences. First, theconsistency of the well-known nearest neighbors classifier (which is notguaranteed in the problems with functional data) is established for theindicated class of processes. Second, and more important, parametric andnonparametric plug-in classifiers can be obtained by estimating the unknownelements in the optimal rule. The performance of these new plug-in classifiersis checked, with positive results, through a simulation study and a real dataexample.

Supervised classification for a family of Gaussian functional models