Non-Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise-Deterministic Markov Processes

Romain Azaïs, François Dufour and Anne Gégout-Petit

Scandinavian Journal of Statistics, 2014, vol. 41, issue 4, 950-969

Abstract: type="main" xml:id="sjos12076-abs-0001">

This paper presents a non-parametric 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 study illustrates the behaviour of our estimator.

Date: 2014
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