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

Romain Azaïs (1, 2) , François Dufour (1, 2) , Anne Gégout-Petit (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability

This paper 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. The paper is illustrated by a numerical example.

Domaines: Théorie [stat.TH]

Romain Azaïs, François Dufour, Anne Gégout-Petit. Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2013, 49 (4), pp.1204-1231. ⟨10.1214/12-AIHP503⟩. ⟨hal-00759062⟩