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View Submission - SDS2022
Title: Learning the regularity of curves in functional data analysis and applications Authors:  Steven Golovkine - University of Limerick (Ireland) [presenting]
Valentin Patilea - CREST-Ensai (France)
Nicolas Klutchnikoff - Universite Rennes 2 (France)
Abstract: 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. The proposed approach is model-free and applies to a large class of stochastic processes. 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, in both cases of differentiable or non-differentiable trajectories.