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

Laetitia Della Maestra and Marc Hoffmann

Stochastic Processes and their Applications, 2023, vol. 155, issue C, 109-146

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.

Keywords: Parametric estimation; LAN property; Maximum likelihood estimation; Statistics and PDE; Interacting particle systems; McKean–Vlasov models (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2022.10.002

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