Nonparametric estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes

Abstract : In this paper, we consider a piecewise deterministic Markov process (PDMP), with known flow and deterministic transition measure, and unknown jump rate $\lambda$. To estimate nonparametrically the jump rate, we first construct an adaptive estimator of the stationary density, then we derive a quotient estimator $\hat{\lambda}_n$ of $\lambda$. We provide uniform bounds for the risk of these estimators, and prove that the estimator of the jump rate is nearly minimax (up to a $\ln^2(n)$ factor). Simulations illustrate the behavior of our estimator.
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Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-01996064
Contributeur : Nathalie Krell <>
Soumis le : lundi 28 janvier 2019 - 10:28:56
Dernière modification le : vendredi 1 février 2019 - 01:20:44

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  • HAL Id : hal-01996064, version 1
  • ARXIV : 1901.10166

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Nathalie Krell, Emeline Schmisser. Nonparametric estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes. 2019. 〈hal-01996064〉

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