Titre: Statistical inference for renewal processes

Summary: We consider nonparametric density estimation for interarrival times density of a renewal process. If it is possible to get continuous observation of the process, then a projection estimator in an orthonormal functional basis can be built. The more realistic setting of discrete time observation is more difficult to handle. If the sampling rate tends to 0, a first strategy consists in neglecting the discretization error. Otherwise, a more precise strategy aims at taking into account the structure of the data: a deconvolution estimator is defined and studied. In that case, we work under a simplifying "dead-zone" condition. In the three cases, an automatic model selection procedure is described and its rate is studied. The results are illustrated through a simulation study. (Joint work with F. Comte)