Rate of estimation for the stationary distribution of jump-processes over anisotropic holder classes

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• dc.contributor.author Amorino, Chiara
• dc.date.accessioned 2025-11-04T17:49:12Z
• dc.date.available 2025-11-04T17:49:12Z
• dc.date.issued 2021
• dc.date.updated 2025-11-04T17:49:12Z
• dc.description.abstract We study the problem of the non-parametric estimation for the density - of the stationary distribution of the multivariate stochastic differential equation with jumps (X), when the dimension d is such that d - 3. From the continuous observation of the sampling path on [0,T]we show that, under anisotropic Hölder smoothness constraints, kernel based estimators can achieve fast convergence rates. In particular, they are as fast as the ones found by Dalalyan and Reiss [11] for the estimation of the invariant density in the case without jumps under isotropic Hölder smoothness constraints. Moreover, they are faster than the ones found by Strauch [32] for the invariant density estimation of continuous stochastic differential equations, under anisotropic Hölder smoothness constraints. Furthermore, we obtain a minimax lower bound on the L2-risk for pointwise estimation, with the same rate up to a log(T ) term. It implies that, on a class of diffusions whose invariant density belongs to the anisotropic Holder class we are considering, it is impossible to find an estimator with a rate of estimation faster than the one we propose.
• dc.description.sponsorship The author gratefully acknowledges financial support of ERC Consolidator Grant 815703 "STAMFORD: Statistical Methods for High Dimensional Diffusions".
• dc.format.mimetype application/pdf
• dc.identifier.citation Amorino C. Rate of estimation for the stationary distribution of jump-processes over anisotropic holder classes. Electron J Stat. 2021;15(2):5067-116. DOI: 10.1214/21-EJS1913
• dc.identifier.doi http://dx.doi.org/10.1214/21-EJS1913
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/71772
• dc.language.iso eng
• dc.publisher Institute of Mathematical Statistics
• dc.relation.ispartof Electronic Journal of Statistics. 2021;15(2):5067-5116
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/815703
• dc.rights Creative Commons Attribution 4.0 International License.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Convergence rate
• dc.subject.keyword Density estimation
• dc.subject.keyword Ergodic diffusion with jumps
• dc.subject.keyword Lévy driven SDE
• dc.subject.keyword Non-parametric statistics
• dc.title Rate of estimation for the stationary distribution of jump-processes over anisotropic holder classes
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion