Sharp adaptive similarity testing with pathwise stability for ergodic diffusions

Abstract: Within the nonparametric diffusion model, we develop a multiple test to infer about similarity of an unknown drift b to some reference drift b_0: At prescribed significance, we simultaneously identify those regions where violation from similarity occurs, without a priori knowledge of their number, size and location. This test is shown to be minimax-optimal and adaptive. At the same time, the procedure is robust under small deviation from Brownian motion as the driving noise process. A detailed investigation for fractional driving noise, which is neither a semimartingale nor a Markov process, is provided for Hurst indices close to the Brownian motion case

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Dissertation, 2022

Classification and Topics

• Keyword: Shāpu-KK ; Stability ; Nichtparametrischer Test ; Diffusionsprozess ; Empirischer Prozess ; Adaptiver Test ; Gebrochene Brownsche Bewegung ; Grenzwertsatz

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2022
• Creator: Brutsche, Johannes
• Contributor: Rohde, Angelika ; Rohde, Angelika ; Trabs, Mathias ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Further information

• DOI: 10.6094/UNIFR/228704
• URN: urn:nbn:de:bsz:25-freidok-2287046
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:53 PM CET