Seminar in applied mathematics and statistics

SPEAKER: Alessia Pini, MOX, Politecnico di Milano

TITLE: Interval-wise testing procedure for domain selection in Functional Data Analysis

ABSTRACT: Inference for functional data embedded in L^2(a,b) is considered, with particular emphasis on the domain selection problem (i.e., detecting the portions of the domain imputable for the rejection of a functional null hypothesis). A general and fully non-parametric approach is presented to achieve that target. The approach, namely interval-wise testing, is based on the introduction of two new inferential tools: the unadjusted and the adjusted p-value functions. After providing their definitions, we 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 provide an overview on some applications in which the unadjusted and the adjusted p-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 tongue profiles 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.

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Tea and chocolate will be served on the 4th floor after the seminar.