B1096
Title: Nonparametric local inference for functional data defined on manifold domains
Authors: Alessia Pini - Universita Cattolica del Sacro Cuore (Italy) [presenting]
Niels Lundtorp Olsen - University of Copenhagen (Denmark)
Simone Vantini - Politecnico di Milano (Italy)
Abstract: A method is proposed to test locally functional data whose domain is a Riemannian manifold. The procedure is based on testing hypotheses on a suitably defined family of balls of the domain and can be applied to a vast variety of different functional tests. For instance, it can be used to compare groups or to test the parameters of a functional regression. The final result is an adjusted p-value function defined on the same domain as functional data, and controlling the ball-wise error rate, which is a suitable extension of family-wise error rate to manifold domains. The procedure is applied to test in three settings: a simulation on a chameleon-shaped manifold, and two applications related to climate change, where the manifolds are a complex subset of $S^2$ and $S^2xS^1$, respectively.
