Depth Measures For Multivariate Functional Data


Statistical learning
Health Analytics
Depth Measures For Multivariate Functional Data
Thursday 10th November 2011
Ieva, F.; Paganoni, A.M.
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The statistical analysis of functional data is a growing interest research area. In particular more and more frequently in the biomedical context the output of many clinical examinations are complex mathematical objects like images or curves. In this work we propose, analyze, and apply a new concept of depth for multivariate functional observations, i.e. statistical units where each component is a curve, in order to study them from a statistical perspective. Robust statistics, such as the median function or trimmed mean, can be generalized to a multivariate functional framework using this new depth measure definition so that outliers detection and nonparametric tests can be carried out also within this more complex context. Mathematical properties of these new concepts are established and proved. Finally, an application to Electrocardiographic (ECG) signals is proposed, aimed at detecting outliers for identifying stable training set to be used in unsupervised classification procedures adopted to perform semi automatic diagnosis and at testing differences between pathological and physiological groups of patients.
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Communication in Statistics – Theory and Methods, 42(7): 1265-1276