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math.ST2025
Smooth and rough paths in mean derivative estimation for functional data
Max Berger, Hajo Holzmann
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional dat…
math.ST2024
Optimal rates for estimating the covariance kernel from synchronously sampled functional data
Max Berger, Hajo Holzmann
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which i…
math.ST2023
From dense to sparse design: Optimal rates under the supremum norm for estimating the mean function in functional data analysis
Max Berger, Philipp Hermann, Hajo Holzmann
We derive optimal rates of convergence in the supremum norm for estimating the Hölder-smooth mean function of a stochastic process which is repeatedly and discretely observed with…