Combining information both within and across trajectories, we propose simple estimators 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. As another application, we build minimax optimal mean and covariance functions estimators. Our estimators perform well in simulations.
Real data sets illustrate the effectiveness of the new approaches.
The talk is based on joint work with Nicolas Klutchnikoff and Steven Golovkine.
Website of Valentin Patilea
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: May 30, 2022, 4.30 pm Vienna
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