Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes
Statistics Theory
2012-07-12 v2 Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1202.2212,
title = {Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes},
author = {Romain Azaïs and François Dufour and Anne Gégout-Petit},
journal= {arXiv preprint arXiv:1202.2212},
year = {2012}
}