Johannes Brutsche:
Sharp adaptive similarity testing with pathwise stability for ergodic diffusions
Time and place
Friday, 17.12.21, 12:00-13:00, online: Zoom
Abstract
Suppose we observe an ergodic diffusion with unknown drift. We develop a fully data-driven nonparametric test for the null hypothesis that the drift is similar to a reference drift under supremum loss. Our procedure turns out to be asymptotically optimal in both rate and constant. Moreover, we investigate its behavior if the true process was driven by a fractional Brownian motion with Hurst index close to 1/2.