Adaptive estimation of the conditional intensity of marker-dependent counting processes

Fabienne Comte (1) , Stéphane Gaïffas (2) , Agathe Guilloux (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.

Domaines: Statistiques [math.ST]

Fabienne Comte, Stéphane Gaïffas, Agathe Guilloux. Adaptive estimation of the conditional intensity of marker-dependent counting processes. 2008. ⟨hal-00333356v1⟩