A1700
Title: Multivariate robust extremiles
Authors: Luca Merlo - Link Campus University (Italy) [presenting]
Valeria Bignozzi - University of Rome Sapienza (Italy)
Lea Petrella - Sapienza University of Rome (Italy)
Nicola Salvati - University of Pisa (Italy)
Abstract: A novel extension of univariate extremiles to a robust multivariate framework is proposed. Among the possible multivariate generalizations, the approach based on multivariate M-quantiles with Huber's multidimensional loss function is adopted. Key theoretical properties of the proposed functional are established, including existence and uniqueness under mild conditions, symmetry relations, location and orthogonal equivariance, and positive homogeneity in limiting cases. The proposed extremile sets lie inside the convex hull of the data while allowing for different levels of robustness. From an inferential perspective, the main asymptotic properties of these robust multivariate extremiles are proven, namely consistency and asymptotic normality, using the theory of Z-estimators. Their empirical performance is assessed through a series of examples on artificial and real-world data.
