Year: 2014
Type: preprint
Abstract: This article addresses the problem of functional supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex empirical risk minimization procedure, and a nonasymptotic oracle inequality is derived. We show that the algorithm provides a Bayes-risk consistent classifier. Furthermore, it is proved that the classifier converges at a rate which adapts to the unknown regularity of the intensity process. Our results are obtained by taking advantage of martingale and stochastic calculus arguments, which are natural in this context and fully exploit the functional nature of the problem.
Source: arXiv (Cornell University)
Authors: Biau, Gérard, Cadre, Benoît, Paris, Quentin
Institutions: Institut Universitaire de France, Université Pierre-et-Marie-Curie, Centre National de la Recherche Scientifique, Centre de Recherche en Économie et Statistique, École Normale Supérieure de Rennes, Institut de recherche mathématique de Rennes, ENSAE Paris, National Research University Higher School of Economics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949905133