Title: Simultaneous inference for function-valued parameters
Authors: Dominik Liebl - University Bonn (Germany) [presenting]
Matthew Reimherr - Pennsylvania State University (United States)
Abstract: A new approach for constructing simultaneous confidence bands for function-valued parameters is presented. The bands are fast to compute as they are based on nearly closed-form expressions and, therefore, do not require computationally expensive resampling based methods. The shape of the bands can be constructed according to a desired criterion specified by the user. A particularly interesting criteria is the proposed concept of ``fair'' or equitable bands, which leads to simultaneous confidence bands that have an adaptive width reflecting the local multiple testing problem. Our bands are constructed by integrating and extending tools from Random Field Theory, an area that has yet to overlap with Functional Data Analysis. Large sample properties are analyzed using asymptotic statistics, and finite-sample properties of our method are investigated by means of extensive simulation studies. Applicability is demonstrated using different real data applications from sports biomechanics and economics.