Nonparametric estimation of the jump rate for piecewise-deterministic Markov processes

Details Nonparametric estimation of the jump rate for piecewise-deterministic Markov processes Nonparametric estimation of the jump rate for piecewise-deterministic Markov processes

2012-02-10

arxiv.org/abs/1202.2212v1

Mathematics

Statistics Theory

Scientific paper

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.

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