A0170
Title: The control of family-wise error rate for functional data: A unified framework
Authors: Alessia Pini - Universita Cattolica del Sacro Cuore (Italy) [presenting]
Konrad Abramowicz - Umea University (Sweden)
Lina Schelin - Umea University (Sweden)
Sara Sjostedt de Luna - Umea University (Sweden)
Aymeric Stamm - CNRS (French National Center for Scientific Research) (France)
Simone Vantini - Politecnico di Milano (Italy)
Abstract: Inference for functional data is currently approached in two different ways: global inference aiming at testing functional hypotheses over the entire domain, and local inference aiming at selecting domain subsets responsible for the rejection of a null hypothesis. In the local setting, a p-value can be computed at every point of the domain, obtaining an unadjusted p-value function, which controls only pointwise the probability of type I error: for all points, the probability of type I error is controlled, but the probability of committing at least one type I error (i.e., the so-called familywise error rate - FWER) is not. Hence, the unadjusted p-value function cannot be used for domain selection purposes, and adjusted p-value functions are needed. A unified framework for methods that fit this purpose is presented. It includes and extends existing methods and our own proposed one. Their inferential properties are characterized in terms of finite-sample or asymptotic control of the FWER and consistency. Finite-sample properties are compared on a simulation study. Finally, the proposed local inferential techniques are applied to knee kinematic and brain tractography data.
