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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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    References listed on IDEAS

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    1. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    2. Li, Zhongyang & Lu, Fei & Maggioni, Mauro & Tang, Sui & Zhang, Cheng, 2021. "On the identifiability of interaction functions in systems of interacting particles," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 135-163.
    3. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261, December.
    4. Wen, Jianghui & Wang, Xiangjun & Mao, Shuhua & Xiao, Xinping, 2016. "Maximum likelihood estimation of McKean–Vlasov stochastic differential equation and its application," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 237-246.
    5. Kay Giesecke & Gustavo Schwenkler & Justin A. Sirignano, 2020. "Inference for large financial systems," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 3-46, January.
    6. Genon-Catalot, Valentine & Larédo, Catherine, 2021. "Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 513-548.
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