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Supervised classification for a family of Gaussian functional models. (English) Zbl 1246.62155

Summary: 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 neighbour classifiers (which is not guaranteed in 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.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62M99 Inference from stochastic processes
62G99 Nonparametric inference
65C60 Computational problems in statistics (MSC2010)
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