IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v155y2023icp109-146.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922002113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.10.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Kay Giesecke & Gustavo Schwenkler & Justin A. Sirignano, 2020. "Inference for large financial systems," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 3-46, January.
    2. 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.
    3. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    4. 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.
    5. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261, December.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amorino, Chiara & Nourdin, Ivan & Shevchenko, Radomyra, 2026. "Fractional interacting particle system: Drift parameter estimation via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    2. 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.
    3. Amorino, Chiara & Gloter, Arnaud & Halconruy, Hélène, 2025. "Evolving privacy: Drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    4. Pavliotis, Grigorios A. & Reich, Sebastian & Zanoni, Andrea, 2025. "Filtered data based estimators for stochastic processes driven by colored noise," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Fabienne Comte & Valentine Genon‐Catalot, 2023. "Nonparametric adaptive estimation for interacting particle systems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1716-1755, December.
    3. Amorino, Chiara & Nourdin, Ivan & Shevchenko, Radomyra, 2026. "Fractional interacting particle system: Drift parameter estimation via Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    4. 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.
    5. Peter Yegon & W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Asset Pricing in the Presence of Market Microstructure Noise," Papers 2511.00308, arXiv.org.
    6. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    7. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    8. Carsten H. Chong & Viktor Todorov, 2023. "Asymptotic Expansions for High-Frequency Option Data," Papers 2304.12450, arXiv.org, revised Feb 2025.
    9. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
    10. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Tito Belchior Silva Moreira & Benjamin Miranda Tabak & Mario Jorge Mendonça & Adolfo Sachsida, 2016. "An Evaluation of the Non-Neutrality of Money," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-20, March.
    12. Attanasio, Orazio & Cattan, Sarah & Fitzsimons, Emla & Meghir, Costas & Rubio-Codina, Marta, 2015. "Estimating the Production Function for Human Capital: Results from a Randomized Control Trial in Colombia," IZA Discussion Papers 8856, IZA Network @ LISER.
    13. Mark P Little & Wolfgang F Heidenreich & Guangquan Li, 2009. "Parameter Identifiability and Redundancy in a General Class of Stochastic Carcinogenesis Models," PLOS ONE, Public Library of Science, vol. 4(12), pages 1-6, December.
    14. Escanciano, Juan Carlos & Hoderlein, Stefan & Lewbel, Arthur & Linton, Oliver & Srisuma, Sorawoot, 2021. "Nonparametric Euler Equation Identification And Estimation," Econometric Theory, Cambridge University Press, vol. 37(5), pages 851-891, October.
    15. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    16. Zadrozny, Peter A., 2022. "Linear identification of linear rational-expectations models by exogenous variables reconciles Lucas and Sims," CFS Working Paper Series 682, Center for Financial Studies (CFS).
    17. Flood, M. D. & Jagadish, H. V. & Raschid, L., 2016. "Big data challenges and opportunities in financial stability monitoring," Financial Stability Review, Banque de France, issue 20, pages 129-142, April.
    18. Peter Davis & Pasquale Schiraldi, 2014. "The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products," RAND Journal of Economics, RAND Corporation, vol. 45(1), pages 32-63, March.
    19. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    20. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:109-146. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.