Title: Functional delta residuals and applications to functional effect sizes
Authors: Fabian Telschow - University of California San Diego (United States) [presenting]
Samuel J Davenport - University of Oxford (United Kingdom)
Armin Schwartzman - University of California, San Diego (United States)
Abstract: Given a functional central limit (fCLT) and a parameter transformation, we use the functional delta method to construct random processes, called functional delta residuals, which asymptotically have the same covariance structure as the transformed limit process. As motivation for this methodology, we provide the formal application of these residuals to a functional version of the effect size parameter Cohen's $d$. We prove a multiplier bootstrap fCLT theorem for these transformed residuals and show how this can be used to construct simultaneous confidence bands (SCBs) for Cohen's $d$. The performance and necessity of such residuals are illustrated in a simulation experiment for the covering rate of SCBs for the functional Cohen's $d$ parameter and an application to CoPE sets in brain imaging is presented.