Component-wise outlier detection methods for robustifying multivariate functional samples

We propose a new method for detecting outliers in multivariate functional data. We exploit the joint use of two different depth measures, and generalize the outliergram to the multivariate functional framework, aiming at detecting and discarding both shape and magnitude outliers. The main application consists in robustifying the reference samples of data, composed by G different known groups to be used, for example, in classification procedures in order to make them more robust. We asses by means of a simulation study the method’s performance in comparison with different outlier detection methods. Finally we consider a real dataset: we classify data minimizing a suitable distance from the center of reference groups. We compare performance of supervised classification on test sets training the algorithm on original dataset and on the robustified one, respectively.