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

01/29/2019

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by   Nathalie Krell, et al.

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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 λ̂_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 ^2(n) factor). Simulations illustrate the behavior of our estimator.