Discussion of “Multivariate functional outlier detection”

Abstract

This interesting paper adds on the authors long and outstanding trajectory in robust statistics and , more specifically, on robust functional data analysis. We congratulate Mia Hubert, Peter Rousseeuw and Pieter Segaert for this important contribution. As the authors point out, most of the literature to date on functional outlier detection deals with univariate functional data (one curve observed by individual). This work considers the case of p-variate functional data (p curves observed by individual). The paper discusses carefully the problem of outlier detection in this setting and starts by establishing a classification of different outlying behaviours. Then, several p-variate functional depths and distance functions are defined by integrating over time the existing or newly defined p-variate counterparts. Finally, by combining these measures, several graphical diagnostic tools are proposed. We would like to contribute to the discussion by focusing on two aspects. Firstly, we will compare the proposed taxonomy of functional outliers with the classification currently adopted in the literature. Secondly, we will comment on the differences between the proposed collection of methods and the outliergram (Arribas-Gil and Romo 2014), the recent procedure to detect shape outliers. We compare it with the proposed methodology in several examples.