The LAN property for McKean-Vlasov models in a mean-field regime - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2023

The LAN property for McKean-Vlasov models in a mean-field regime

Résumé

We establish the local asymptotic normality (LAN) property for estimating a multidimensional parameter in the drift of a system of $N$ interacting particles observed over a fixed time horizon in a mean-field regime $N \rightarrow \infty$. By implementing the classical theory of Ibragimov and Hasminski, we obtain in particular sharp results for the maximum likelihood estimator that go beyond its simple asymptotic normality thanks to H\'ajek's convolution theorem and strong controls of the likelihood process that yield asymptotic minimax optimality (up to constants). Our structural results shed some light to the accompanying nonlinear McKean-Vlasov experiment, and enable us to derive simple and explicit criteria to obtain identifiability and non-degeneracy of the Fisher information matrix. These conditions are also of interest for other recent studies on the topic of parametric inference for interacting diffusions.

Dates et versions

hal-03950980 , version 1 (22-01-2023)

Identifiants

Citer

Laetitia Della Maestra, Marc Hoffmann. The LAN property for McKean-Vlasov models in a mean-field regime. Stochastic Processes and their Applications, 2023, ⟨10.1016/j.spa.2022.10.002⟩. ⟨hal-03950980⟩
23 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More