  The paper introduces a method to construct confidence bands for bounded,
band-limited functions based on a finite sample of input-output pairs. The
approach is distribution-free w.r.t. the observation noises and only the
knowledge of the input distribution is assumed. It is nonparametric, that is,
it does not require a parametric model of the regression function and the
regions have non-asymptotic guarantees. The algorithm is based on the theory of
Paley-Wiener reproducing kernel Hilbert spaces. The paper first studies the
fully observable variant, when there are no noises on the observations and only
the inputs are random; then it generalizes the ideas to the noisy case using
gradient-perturbation methods. Finally, numerical experiments demonstrating
both cases are presented.
