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Article Dans Une Revue Electronic Journal of Statistics Année : 2022

Learning the smoothness of noisy curves with application to online curve estimation

Résumé

Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time points. Non-asymptotic bounds for the concentration of the estimator are derived. Given the estimate of the local regularity, we build a nearly optimal local polynomial smoother from the curves from a new, possibly very large sample of noisy trajectories. We derive non-asymptotic pointwise risk bounds uniformly over the new set of curves. Our estimates perform well in simulations. Real data sets illustrate the effectiveness of the new approaches.

Dates et versions

hal-03385816 , version 1 (19-10-2021)

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Steven Golovkine, Nicolas Klutchnikoff, Valentin Patilea. Learning the smoothness of noisy curves with application to online curve estimation. Electronic Journal of Statistics , 2022, 16 (1), pp.1485-1560. ⟨10.1214/22-EJS1997⟩. ⟨hal-03385816⟩
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