title: The interval testing procedure: A general framework for inference in functional data analysis.
abstract: We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted p-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package.
authors.affiliation: MOX-Department of Mathematics, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy. alessia.pini@polimi.it.
authors.forename: Alessia
authors.initials: A
authors.lastname: Pini
authors.affiliation: MOX-Department of Mathematics, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy. simone.vantini@polimi.it.
authors.forename: Simone
authors.initials: S
authors.lastname: Vantini
mesh_terms: D000465:Algorithms; D002339:Carotid Arteries / Q000473:pathology / Q000503:physiopathology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006439:Hemodynamics; D006801:Humans; D002532:Intracranial Aneurysm / Q000473:pathology; D015233:Models, Statistical
keywords: Family wise error rate; Functional data analysis; Inference; Multiple comparison; Permutation method