B0649
Title: Robust fitting of wrapped models to multivariate torus data
Authors: Luca Greco - University G. Fortunato of Benevento (Italy) [presenting]
Claudio Agostinelli - University of Trento (Italy)
Giovanni Saraceno - University of Trento (Italy)
Abstract: Multivariate circular data arise commonly in many different fields. Depending on the situation, observations can be thought of as points on the surface of a $p$-dimensional torus. The peculiarity of multivariate torus data is periodicity, which reflects in the boundedness of the sample space and often of the parametric space. Multivariate torus data are not immune to the occurrence of outliers, such as unexpected angles or directions that do not share the main pattern of the bulk of the data. Hence, a likelihood-based estimation can be badly affected, leading to unreliable results. Therefore, robust methods are needed to handle such data inadequacies with a twofold aim: lead to a robust parametric fit that is reliable under contamination and provide a testing strategy to detect outliers. Robust estimation is pursued according to a general CEM-type algorithm. In the CE step, data are suitably unwrapped on a flat torus, then the M-step is enhanced by the computation of a set of data-dependent weights aimed to down-weight outliers and mitigate their effect on the fit. We discuss and compare different strategies to measure outlyingness and evaluate weights. On the other hand, outliers detection can rely on formal rules and be based on the inspection of robust distances, rather than on weights, stemming from the robust fit.
