BIRS Workshop Lecture Videos
Non-parametric multi-aspect local null hypothesis testing for functional data Vantini, Simone
In the talk, we will present and discuss a general framework for multi-aspect local non-parametric null-hypothesis testing for functional data defined on a common domain (Pini and Vantini, 2017). In detail: “multi-aspect” pertains to the fact the procedure allows the simultaneous investigation of many different data aspects like means, variances, quantiles of functional data and their associated differential and/or integral quantities; “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 functional one-way ANOVA with an application 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 (Pini et al. 2017a). Finally, we will quickly show how to extend the approach to deal with more complex testing problems like functional two-way ANOVA and functional-on-scalar linear regression with applications to the analysis of spectral data (Pini et al. 2017b) and human movement data (Pini et al. 2015), respectively. Hébert-Losier, K., Pini, A., Vantini, S., Strandberg, J., Abramowicz, K., Schelin, L., Häger, C. K. (2015): "One-leg hop kinematics 20 years following anterior cruciate ligament rupture: Data revisited using functional data analysis", Clinical Biomechanics, Vol. 30(10), pp. 1153-1161. Pini, A., Vantini, S. (2017): “Interval-Wise Testing for Functional Data”, Journal of Nonparametric Statistics. 29 (2), pp. 407-424. Pini, A., Spreafico, L., Vantini, S., Vietti, A. (2017): Multi-aspect local inference for functional data: analysis of ultrasound tongue profiles. Tech. Rep. MOX 28/2017, Dept. of Mathematics, Politecnico di Milano (https://mox.polimi.it). Pini, A., Vantini, S., Colosimo, B. M., Grasso, M. (2017): “Domain-Selective Functional Analysis of Variance for Supervised Statistical Profile Monitoring of Signal Data”, Journal of the Royal Statistical Society – Series C (to appear).
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