Local Hypothesis Testing for Functional Data: Extending False Discovery Rate to the Functional Framework

A topic which is becoming more and more popular in Functional Data Analysis is local inference, i.e., the continuous statistical testing of a null hypothesis along the domain. This can be seen as an extreme case of the multiple comparison problem. During the talk, we will define and discuss the notion of False Discovery Rate (FDR) in the setting of functional data.We will then introduce a new procedure (i.e., a continuous version of the Benjamini-Hochberg procedure) able to control the FDR over the functional domain, describe its properties in terms of control of the Type-I error probability and of consistency. The proposed method will be applied to satellite measurements of Earth temperature with the aim of identifying the regions of the planet where temperature has significantly increased in the last decades.