CONSISTENT PROCEDURES FOR MULTICLASS CLASSIFICATION OF DISCRETE DIFFUSION PATHS

Christophe Denis (1) , Charlotte Dion (2) , Miguel Martinez (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Mots clés: Multiclass classification; diffusion paths; plug-in estimators; drift estimation; empirical risk minimization

Domaines: Théorie [stat.TH]

Christophe Denis, Charlotte Dion, Miguel Martinez. CONSISTENT PROCEDURES FOR MULTICLASS CLASSIFICATION OF DISCRETE DIFFUSION PATHS. 2018. ⟨hal-01869545v1⟩