B0582
Title: False discovery rate for functional data
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 topic that is becoming more and more popular in Functional Data Analysis is local inference, i.e., the continuous statistical testing of a null hypothesis along with a domain of interest. The principal issue in this field is the infinite amount of tests to perform, which can be seen as an extreme case of multiple comparisons problem. A number of quantities have been introduced in the literature of multivariate analysis in relation to the multiple comparisons problem. Arguably the most popular one is the False Discovery Rate (FDR), which measures the expected proportion of false discoveries among all discoveries. FDR is defined in the setting of functional data defined on a compact set of $R^d$, and we further generalize this definition to functional data defined on a manifold. A continuous version of the Benjamini-Hochberg method is introduced, along with a definition of adjusted p-value function. Some general conditions are stated, under which the functional Benjamini-Hochberg (fBH) procedure provides control of FDR. We show how the procedure can be plugged-in with every parametric or nonparametric pointwise test, given that such test is exact. Finally, to show the practical usefulness of our procedure, the proposed method is applied to the analysis of a data set of daily temperatures on the Earth to identify the regions where the temperature has significantly increased over the last decades.
