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Angelika Rohde (University of Freiburg) “Sharp adaptive similarity testing with pathwise stability for ergodic diffusions”

November 28 @ 2:00 pm - 3:15 pm

Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 28th of Novembre 2022
Place: Room 3001

Angelika Rohde (University of Freiburg) “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.

 

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)
Sponsors:
CREST-CMAP