IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v51y2024i3p1103-1160.html
   My bibliography  Save this article

Nonparametric plug‐in classifier for multiclass classification of S.D.E. paths

Author

Listed:
  • Christophe Denis
  • Charlotte Dion‐Blanc
  • Eddy Ella‐Mintsa
  • Viet Chi Tran

Abstract

We study the multiclass classification problem where the features come from a mixture of time‐homogeneous diffusions. Specifically, the classes are discriminated by their drift functions while the diffusion coefficient is common to all classes and unknown. In this framework, we build a plug‐in classifier which relies on nonparametric estimators of the drift and diffusion functions. We first establish the consistency of our classification procedure under mild assumptions and then provide rates of convergence under different set of assumptions. Finally, a numerical study supports our theoretical findings.

Suggested Citation

  • Christophe Denis & Charlotte Dion‐Blanc & Eddy Ella‐Mintsa & Viet Chi Tran, 2024. "Nonparametric plug‐in classifier for multiclass classification of S.D.E. paths," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1103-1160, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:1103-1160
    DOI: 10.1111/sjos.12702
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12702
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12702?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
    ---><---

    References listed on IDEAS

    as
    1. Pierre Lafaye de Micheaux & Pavlo Mozharovskyi & Myriam Vimond, 2021. "Depth for Curve Data and Applications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1881-1897, October.
    2. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    3. Hoffmann, Marc, 1999. "Adaptive estimation in diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 135-163, January.
    4. F. Comte & V. Genon-Catalot, 2020. "Regression function estimation as a partly inverse problem," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1023-1054, August.
    5. Christophe Denis & Charlotte Dion & Miguel Martinez, 2020. "Consistent procedures for multiclass classification of discrete diffusion paths," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 516-554, June.
    Full references (including those not matched with items on IDEAS)

    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. Eddy Ella-Mintsa, 2024. "Nonparametric estimation of the diffusion coefficient from i.i.d. S.D.E. paths," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 585-640, October.
    2. Nicolas Marie, 2023. "Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models," Finance and Stochastics, Springer, vol. 27(1), pages 97-126, January.
    3. Comte, Fabienne & Genon-Catalot, Valentine, 2021. "Drift estimation on non compact support for diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 174-207.
    4. Comte, Fabienne & Marie, Nicolas, 2023. "Nonparametric drift estimation from diffusions with correlated Brownian motions," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    5. Charlotte Dion & Sarah Lemler, 2020. "Nonparametric drift estimation for diffusions with jumps driven by a Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 489-515, October.
    6. Christophe Denis & Charlotte Dion & Miguel Martinez, 2020. "Consistent procedures for multiclass classification of discrete diffusion paths," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 516-554, June.
    7. Fujii, Masaaki & Takahashi, Akihiko, 2019. "Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1492-1532.
    8. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    9. Fan, ShengJun, 2016. "Existence of solutions to one-dimensional BSDEs with semi-linear growth and general growth generators," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 7-15.
    10. Masaaki Fujii & Akihiko Takahashi, 2015. "Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 283-304, September.
    11. Kupper, Michael & Luo, Peng & Tangpi, Ludovic, 2019. "Multidimensional Markovian FBSDEs with super-quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 902-923.
    12. Mingyu Xu, 2007. "Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 1005-1039, December.
    13. Gobet, Emmanuel & Labart, Céline, 2007. "Error expansion for the discretization of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 803-829, July.
    14. Han, Xingyu, 2018. "Pricing and hedging vulnerable option with funding costs and collateral," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 103-115.
    15. Giorgia Callegaro & Alessandro Gnoatto & Martino Grasselli, 2021. "A Fully Quantization-based Scheme for FBSDEs," Working Papers 07/2021, University of Verona, Department of Economics.
    16. Dirk Becherer & Wilfried Kuissi-Kamdem & Olivier Menoukeu-Pamen, 2023. "Optimal consumption with labor income and borrowing constraints for recursive preferences," Working Papers hal-04017143, HAL.
    17. Qi Zeng & Hae Won (Henny) Jung, 2014. "Optimal Contract, Ownership Structure and Asset Pricing," 2014 Meeting Papers 911, Society for Economic Dynamics.
    18. Shaolin Ji & Xiaomin Shi, 2016. "Explicit solutions for continuous time mean-variance portfolio selection with nonlinear wealth equations," Papers 1606.05488, arXiv.org.
    19. Alessandro Gnoatto & Athena Picarelli & Christoph Reisinger, 2020. "Deep xVA solver -- A neural network based counterparty credit risk management framework," Papers 2005.02633, arXiv.org, revised Dec 2022.
    20. Luis Escauriaza & Daniel C. Schwarz & Hao Xing, 2020. "Radner equilibrium and systems of quadratic BSDEs with discontinuous generators," Papers 2008.03500, arXiv.org, revised May 2021.

    More about this item

    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:bla:scjsta:v:51:y:2024:i:3:p:1103-1160. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.