What question did this study set out to answer?

The aim is to determine optimal rates of convergence for estimating partial derivatives of mean functions in functional data analysis.

Smooth and Rough Sample Paths in Mean Derivative Estimation for Functional Data

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This analysis evaluates derivative estimation in functional data, revealing implications for data dynamics.

The aim is to determine optimal rates of convergence for estimating partial derivatives of mean functions in functional data analysis.
Derived near-optimal convergence rates in a multivariate setting.
Conducted analysis under Hölder smoothness classes.
Implemented a multivariate local polynomial derivative estimator.
Derived a central limit theorem for continuous functions in the sup-norm.
Obtained slower convergence rates for processes with rough sample paths.
Achieved parametric rates for smoother sample paths under dense design conditions.
Illustrated finite-sample performance in simulations and real data applications.

Berger et al. (2026) studied this question.

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