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arXiv · 2508.05259

Nonparametric Estimation from Correlated Copies of a Drifted Process

Nicolas Marie
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Abstract

This paper presents several situations leading to the observation of multiple correlated copies of a drifted process, and then non-asymptotic risk bounds are established on nonparametric estimators of the drift function $b_0$ and its derivative. For drifted Gaussian processes with a regular enough covariance function, a sharper risk bound is established on the estimator of $b_0'$, and a model selection procedure is provided with theoretical guarantees.

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Nicolas Marie. 2025-08-07. Nonparametric Estimation from Correlated Copies of a Drifted Process. https://doi.org/10.1016/j.jmva.2026.105607

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