AZAÏS, Romain; DUFOUR, François; GÉGOUT-PETIT, Anne

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AZAÏS, Romain
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

DUFOUR, François
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

GÉGOUT-PETIT, Anne
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

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This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation example illustrates the behavior of our estimator.< Réduire

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Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes

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