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Abstract:
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Bayes classifiers for functional data pose a challenge because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We construct Bayes classifiers using density ratios of projections on a sequence of eigenfunctions that are common to the groups to be classified. In the large sample limit, our classifiers have misclassification rate converging to zero under certain conditions, and they also perform favorably in comparisons with other functional classifiers in simulations and various data applications.
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