A1265
Title: Sharp adaptive similarity testing with pathwise stability for ergodic diffusions
Authors: Johannes Brutsche - University of Freiburg (Germany) [presenting]
Angelika Rohde - University of Freiburg (Germany)
Abstract: Within the nonparametric diffusion model, multiple tests are developed to infer the similarity of an unknown drift $b$ to some reference drift $b_0$: At prescribed significance, those regions are simultaneously identified 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 deviations 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.
