Section: New Results

Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes.

Participants : Romain Azais, François Dufour, Anne Gégout-Petit.

Non-homogeneous marked renewal process, nonparametric estimation, jump rate estimation, Nelson-Aalen estimator, asymptotic consistency, ergodicity of Markov chains

This work is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. A numerical example illustrates our theoretical results.

It has been published in Ann. Inst. H. Poincaré Probab. Statist. [16] .