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Statistical learning for $$\psi $$ ψ -weakly dependent processes

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  • Mamadou Lamine Diop

    (Université Gaston Berger)

  • William Kengne

    (Universite Claude Bernard Lyon 1)

Abstract

The purpose of this paper is to study the generalization performance of the Empirical Risk Minimization (ERM) algorithm from $$\psi $$ ψ -weakly dependent processes. These processes unify a large class of weak dependence conditions, including strong mixing and association. We first establish the exponential bound on the rate of relative uniform convergence and the consistency of the ERM algorithm. Secondly, we derive generalization bounds and provide the learning rate. Under some Hölder class of hypothesis, we obtain an asymptotic rate close to $$O(n^{-1/2})$$ O ( n - 1 / 2 ) . Finally, we present some application and simulation results with examples of causal models within the context of time series prediction.

Suggested Citation

  • Mamadou Lamine Diop & William Kengne, 2025. "Statistical learning for $$\psi $$ ψ -weakly dependent processes," Statistical Inference for Stochastic Processes, Springer, vol. 28(2), pages 1-23, August.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:2:d:10.1007_s11203-025-09329-6
    DOI: 10.1007/s11203-025-09329-6
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    References listed on IDEAS

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    6. Francq, Christian & Thieu, Le Quyen, 2019. "Qml Inference For Volatility Models With Covariates," Econometric Theory, Cambridge University Press, vol. 35(1), pages 37-72, February.
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