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

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  • 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
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    References listed on IDEAS

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    3. 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.
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    1. Eddy-Michel Ella-Mintsa, 2025. "Minimax rates of convergence for the nonparametric estimation of the diffusion coefficient from time-homogeneous SDE paths," Statistical Inference for Stochastic Processes, Springer, vol. 28(3), pages 1-49, December.

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