A0219
Title: The control of the false discovery rate for functional data defined over 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: Inference for functional data can be approached by either a global or a local perspective. In the case of local inference, a single test is performed on the entire domain. In the case of local inference instead, a p-value function is defined, assigning a p-value to each point of the domain, in order to select the portions of it responsible for the rejection of a null hypothesis. In the local setting, it is straightforward to compute a p-value at every point of the domain, obtaining an unadjusted p-value function, which controls only pointwise the probability of type I error. However, one of the main issues in this framework is how to efficiently adjust such function, in order to provide an error control over the entire domain. The focus is on the control of the false discovery rate (FDR). First, the classical notion of FDR is extended to functional data. Further, a continuous version of the Benjamini-Hochberg procedure is introduced, along with a definition of adjusted p-value function. Some general conditions are stated, under which the functional Benjamini-Hochber procedure provides control of FDR. The procedure is very general, and can be applied also to functional data defined in complex domains such as manifolds. Finally, the proposed method is applied to satellite measurements of Earth temperature. In detail, we aim at identifying the regions of the planet where temperature has significantly increased in the last decades.
