Supervised Classification for a Family of Gaussian Functional Models |
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Authors: | AMPARO BAÍLLO ANTONIO CUEVAS JUAN ANTONIO CUESTA‐ALBERTOS |
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Institution: | 1. Departamento de Matemáticas, Universidad Autónoma de Madrid;2. Departamento de Matemáticas, Universidad de Cantabria |
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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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Keywords: | discrimination functional data Gaussian processes Radon– Nikodym derivative |
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