Statistical learning for ψ-weakly dependent processes

09/30/2022

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by   Mamadou Lamine Diop, et al.

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We consider statistical learning question for ψ-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,⋯ The consistency of the empirical risk minimization algorithm is established. We derive the generalization bounds and provide the learning rate, which, on some Hölder class of hypothesis, is close to the usual O(n^-1/2) obtained in the i.i.d. case. Application to time series prediction is carried out with an example of causal models with exogenous covariates.