Discussion of "multivariate functional outlier detection" by M. Hubert, P. Rousseeuw and P. Segaert

I would like to congratulate M. Hubert, P. Rousseeuw and P. Segaert for this stimulating and useful work on outlier detection methods for multivariate functional data. They define and classify rigorously different types of functional outliers and propose several techniques for detecting them in multivariate functional data. These authors use the notion of data depth and distances derived from them to develop statistical and graphical tools to detect and visualize potential outliers. Several important ideas are emphasized in this paper. First, it is shown that there are many different ways of being outlier when dealing with multivariate functional data and that multivariate outliers do not necessarily have to be marginal outliers. Second, depth alone does not always provide sufficient information for detecting outliers, and some distance-based ranking is needed. The authors present several approaches for outlier detection and visualization. One uses a proposed bagdistance based on the center and dispersion provided by the multivariate funtional halfspace depth introduced in Claeskens et al. (2014). Another approach uses a skew-adjusted projection depth that can be extended to multivariate functional data. Several diagnostic and exploratory tools based on these notions are proposed and analyzed.