Semiparametric inference for the recurrent event process by means of a single-index model

Olivier Bouaziz (1) , Ségolen Geffray (2) , Olivier Lopez (3, 4)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 IRMA - Institut de Recherche Mathématique Avancée
3 CREST - Centre de Recherche en Économie et Statistique
4 LSTA - Laboratoire de Statistique Théorique et Appliquée

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumulative mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a reduction dimension technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensionality when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results.

Keywords: single-index model; asymptotic normality; dimension reduction; empirical processes; recurrent events; right-censoring; single-index model.

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Olivier Bouaziz, Ségolen Geffray, Olivier Lopez. Semiparametric inference for the recurrent event process by means of a single-index model. 2014. ⟨hal-00446528v2⟩