Date/heure
11 avril 2024
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Mark Podolskij
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
This paper 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.