Statistica Sinica 23 (2013), 635-665

NONPARAMETRIC ESTIMATION OF THE INTENSITY

FUNCTION OF A RECURRENT EVENT PROCESS

Olivier Bouaziz$^1$, Fabienne Comte$^2$ and Agathe Guilloux$^3$

$^{1}$MAP$5$, UMR CNRS $8145$, University and IUT Paris Descartes,

$^2$MAP$5$, UMR CNRS $8145$ and University Paris Descartes

and $^{3}$LSTA, University Pierre et Marie Curie

Abstract: In this paper, we consider estimating the intensity of a recurrent event process observed under a standard censoring scheme. We first propose a collection of kernel estimators for which we provide MSE and MISE bounds. We then describe and study an adaptive procedure of bandwidth selection, in the spirit of Goldenshluger and Lepski (2010), and prove an oracle type bound for both the MSE and the MISE of the final estimator. The method is illustrated by simulation experiments.

Key words and phrases: Adaptive estimation, censoring, intensity, kernel estimator, nonparametric estimation, recurrent event process.