Fast and fair simultaneous confidence bands for functional parameters

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