B1157
Title: Inference for functional data using the adjusted $p$-value function
Authors: Simone Vantini - Politecnico di Milano (Italy) [presenting]
Alessia Pini - Universita Cattolica del Sacro Cuore (Italy)
Abstract: Inference for functional data embedded in $L^2(a,b)$ is considered, with particular emphasis on the domain selection problem (i.e., detecting those portions of the domain where a given functional null hypothesis is rejected). We will present a general and fully non-parametric approach to achieve that target that is based on the introduction of two new inferential tools: the unadjusted and the adjusted $p$-value functions. After providing their definitions, we will describe their inferential properties in terms of control of the Type-I error probability and of consistency (point-wise and interval-wise, respectively). Finally, to show the flexibility of the methodology we will provide an overview on some applications in which the \textit{unadjusted} and the \textit{adjusted} $p$\textit{-value functions} have been used to face different testing problems such to answer specific research questions pointed out by experts: two-population test for pair-wise comparison of the tongue movements in different experimental settings; functional analysis of variance of reflectance spectra for selecting frequency bands for remote monitoring of laser welding; functional-on-scalar linear model of body part trajectories for the long-term assessment of therapies to fix Anterior Cruciate Ligament injuries.
