  Quantifying uncertainty using confidence regions is a central goal of
statistical inference. Despite this, methodologies for confidence bands in
Functional Data Analysis are still underdeveloped compared to estimation and
hypothesis testing. In this work, we present a new methodology for constructing
simultaneous confidence bands for functional parameter estimates. Our bands
possess a number of positive qualities: (1) they are not based on resampling
and thus are fast to compute, (2) they are constructed under the fairness
constraint of balanced false positive rates across partitions of the bands'
domain which facilitates the typical global, but also novel local
interpretations, and (3) they do not require an estimate of the full covariance
function and thus can be used in the case of fragmentary functional data.
Simulations show the excellent finite-sample behavior of our bands in
comparison to existing alternatives. The practical use of our bands is
demonstrated in two case studies on sports biomechanics and fragmentary growth
curves.
