Thursday, November 28, 2024 - 16:15 in T2-234
On nonparametric estimation of the interaction function in particle system models
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Denis Belomestny from Universität Duisburg-Essen
| Abstract: |
This talk delves into a challenging problem of nonparametric estimation for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an analysis of the stochastic and approximation errors associated with both procedures, along with an examination of certain minimax lower bounds. In particular, for the first method we show that there is a natural metric under which the corresponding estimation error of the interaction function converges to zero with parametric rate which is minimax optimal. This result is rather surprising given the complexity of the underlying estimation problem and rather large class of interaction functions for which the above parametric rate holds.
|
Back
