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Supervised Classification for a Family of Gaussian Functional Models
Author(s) -
BAÍLLO AMPARO,
CUEVAS ANTONIO,
CUESTAALBERTOS JUAN ANTONIO
Publication year - 2011
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00734.x
Subject(s) - mathematics , gaussian , classifier (uml) , parametric statistics , covariance , classification rule , consistency (knowledge bases) , artificial intelligence , gaussian process , pattern recognition (psychology) , class (philosophy) , one class classification , machine learning , data mining , computer science , statistics , discrete mathematics , physics , quantum mechanics
. 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.