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Supervised Classification for a Family of Gaussian Functional Models

Authors


Amparo Baíllo, Departamento de Matemáticas, Fac. Ciencias, Universidad Autónoma de Madrid, 28049-Madrid, Spain.
E-mail: amparo.baillo@uam.es

Abstract

Abstract.  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 neighbours 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 non-parametric 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.

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