Asymptotic equivalence for pure jump L\'evy processes with unknown L\'evy density and Gaussian white noise

  title={Asymptotic equivalence for pure jump L\'evy processes with unknown L\'evy density and Gaussian white noise},
  author={Ester Mariucci},
  journal={arXiv: Probability},
Spectral-free estimation of L\'evy densities in high-frequency regime
We construct an estimator of the L\'evy density of a pure jump L\'evy process, possibly of infinite variation, from the discrete observation of one trajectory at high frequency. The novelty of our
Asymptotic equivalence for density estimation and gaussian white noise: An extension
The aim of this paper is to present an extension of the well-known as-ymptotic equivalence between density estimation experiments and a Gaussian white noise model by enlarging the nonparametric class of the admissible densities.
Compound Poisson approximation to estimate the Lévy density
We construct an estimator of the Levy density, with respect to the Lebesgue measure, of a pure jump Levy process from high frequency observations: we observe one trajectory of the Levy process over
Efficient nonparametric inference for discretely observed compound Poisson processes
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and Lévy distributions are proposed and functional
Classical robots perturbed by Lévy processes: analysis and Lévy disturbance rejection methods
The stability and convergence of state, disturbance and parametric estimates of a robot have been analyzed using the Lyapunov method in the existing literature. In this paper, we analyze the problem
Strong Gaussian approximation of the mixture Rasch model
It is proved that the mixture Rasch model is asymptotically equivalent to a Gaussian observation scheme in Le Cam's sense as n tends to infinity and m is allowed to increase slowly in n.
of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Seven Number Four November 2021
The papers published in Bernoulli are indexed or abstracted in Current Index to Statistics, Mathematical Reviews, Statistical Theory and Method Abstracts-Zentralblatt (STMA-Z), and Zentralblatt für
of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Five Number Two May 2019
  • 2019


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