Multi-aspect local inference for functional data: analysis of ultrasound tongue profiles
Saturday 10th June 2017
Pini, A.; Spreafico, L.; Vantini, S.; Vietti, A.
Motivated by the functional data analysis of a data set of ultrasound tongue profiles, we present the multi-aspect interval-wise testing (multi-aspect IWT), i.e., a local non-parametric inferential technique for functional data embedded in Sobolev spaces. Multi-aspect IWT is a non-parametric procedure that tests differences between groups of functional data jointly taking into account the curves and their derivatives. The multi-aspect IWT provides adjusted multi-aspect p-value functions that can be used to select intervals of the domain imputable for the rejection of a null hypothesis. As a result, it can impute the rejection of a functional null hypothesis to specific intervals of the domain and to specific orders of differentiation. We show that the multi-aspect p-value functions are provided with a control of the family-wise error rate, and are consistent. We apply the multi-aspect IWT to the functional data analysis of a data set of tongue profiles recorded for a study on Tyrolean, a German dialect spoken in South Tyrol. We test differences between five different manners of articulation of uvular rhotics: trill, tap, fricative, approximant, and vocalized /r/. Multi-aspect IWT-based comparisons result in an informative and detailed representation of the regions of the tongue where a significant difference is located.