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.

中文翻译：

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用于增强多元功能样本的分量异常值检测方法

我们提出了一种检测多元函数数据中异常值的新方法。我们利用两种不同深度度量的联合使用，并将异常值推广到多元函数框架，旨在检测和丢弃形状和幅度异常值。主要应用包括增强由 G 不同已知组组成的数据参考样本，例如，在分类程序中使用，以使它们更健壮。我们通过模拟研究与不同的异常值检测方法相比，评估了该方法的性能。最后，我们考虑一个真实的数据集：我们对数据进行分类，以最小化与参考组中心的合适距离。