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

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  • Della Maestra, Laetitia
  • Hoffmann, Marc

Abstract

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→∞. 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 Hájek’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.

Suggested Citation

  • Della Maestra, Laetitia & Hoffmann, Marc, 2023. "The LAN property for McKean–Vlasov models in a mean-field regime," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 109-146.
    • Handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:109-146
    DOI: 10.1016/j.spa.2022.10.002
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    Cited by:

    1. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.
    2. Sharrock, Louis & Kantas, Nikolas & Parpas, Panos & Pavliotis, Grigorios A., 2023. "Online parameter estimation for the McKean–Vlasov stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 481-546.

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