Discussion of “ Multivariate functional outlier detection ” by Mia Hubert , Peter Rousseeuw and Pieter Segaert

Mia Hubert, Peter Rousseeuw and Pieter Segaert (subsequently HRS) are to be praised for having developed a visual and well applicable methodology of treating outliers in functional data. Their principal achievements include a systematics of functional outliers, novel visualizations and a measure of outlyingness (bagdistance), which nicely combines Euclidean distance with location depth. Most important, the authors offer a consequent multivariate view on the functions, either assuming genuinely multidimensional functions or considering multiple aspects of such functions. Several real-data examples illuminate the capacity and the possible output of the new procedures. Also, an R-package of the methodology is announced, which will be greatly welcomed. In the following remarks, I shall first try to put the new methodology into a broader context of outlier search. Then some specifics of functional data are discussed, which call for particular treatments. Third a refined approach is sketched that considers integrals over subintervals. Finally, I will address the use of different functional depth notions and the computational problems arising with them.