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arXiv · 1901.10166

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

Nathalie Krell·Emeline Schmisser
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Abstract

In this paper, we consider a piecewise deterministic Markov process (PDMP), with known flow and deterministic transition measure, and unknown jump rate $λ$. To estimate nonparametrically the jump rate, we first construct an adaptive estimator of the stationary density, then we derive a quotient estimator $\hatλ_n$ of $λ$. 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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Nathalie Krell, Emeline Schmisser. 2020-12-08. Nonparametric estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes. https://arxiv.org/abs/1901.10166

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