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Consistent procedures for multiclass classification of discrete diffusion paths
Author(s) -
Denis Christophe,
Dion Charlotte,
Martinez Miguel
Publication year - 2020
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/sjos.12415
Subject(s) - mathematics , context (archaeology) , multiclass classification , consistency (knowledge bases) , bayes' theorem , parametric statistics , minification , mathematical optimization , algorithm , data mining , machine learning , computer science , bayesian probability , statistics , support vector machine , geometry , paleontology , biology
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.