Consistent procedures for multiclass classification of discrete diffusion paths

The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule....

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Bibliographic Details
Published inScandinavian journal of statistics Vol. 47; no. 2; pp. 516 - 554
Main Authors Denis, Christophe, Dion, Charlotte, Martinez, Miguel
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.06.2020
Wiley
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ISSN0303-6898
1467-9469
DOI10.1111/sjos.12415

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Summary:The recent advent of modern technology has generated a large number of datasets which can be frequently modeled as functional data. This paper focuses on the problem of multiclass classification for stochastic diffusion paths. In this context we establish a closed formula for the optimal Bayes rule. We provide new statistical procedures which are built either on the plug‐in principle or on the empirical risk minimization principle. We show the consistency of these procedures under mild conditions. We apply our methodologies to the parametric case and illustrate their accuracy with a simulation study through examples.
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ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12415