Title: Non-parametric multi-aspect local null hypothesis testing for functional data: Analysis of articulatory phonetics data
Authors: Alessia Pini - Università Cattolica del Sacro Cuore (Italy)
Lorenzo Spreafico - Free University of Bozen-Bolzano (Italy)
Simone Vantini - Politecnico di Milano (Italy) [presenting]
Alessandro Vietti - Free University of Bozen-Bolzano (Italy)
Abstract: The focus is on the statistical comparison of ultrasound tongue profiles pertaining to different allophones pronounced by the same speaker which can be modelled as functions varying on a spatio-temporal domain. Stimulated by this application we will introduce a general framework for multi-aspect local non-parametric null-hypothesis testing for functional data. In detail: ``multi-aspect'' pertains to the fact the procedure allows the simultaneous investigation of many different data aspects like means and variances of tongue vertical position, slope, concavity, velocity, and acceleration; ``local'' pertains instead to the fact the procedure can impute the rejection to aspect-specific regions of the domain; finally, ``non-parametric'' refers to the fact that the specific implementation of the procedure is permutation-based and thus finite-sample exact and consistent independently on data Gaussianity. For ease of clarity, the focus will be on functional two-population tests and ANOVA. Nevertheless, the approach is flexible enough to be adapted to more complex testing problems like functional linear regression.