Nonparametric Estimation from Correlated Copies of a Drifted Process

Nicolas Marie

doi:10.1016/j.jmva.2026.105607

paper

Nonparametric Estimation from Correlated Copies of a Drifted Process

arXiv:2508.05259 · doi:10.1016/j.jmva.2026.105607

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.

23 pages, 6 figures

References in corpus (1)

Nonparametric Estimation for I.I.D. Paths of a Martingale Driven Model with Application to Non-Autonomous Financial Models