Dipartimento di Scienze Statistiche

PhD program in Statistics DSS Statistics Seminar    In person.Room 24 (CU002)   Webinar^.https://uniroma1.zoom.us/j/86881977368?pwd=SWRFc VFjMDZTa0lXZk05TE1zNm5adz09 Passcode: 432940 Abstract Directional distribution depth function and its application to classification Cinzia Viroli Dipartimento di Scienze Statistiche "Paolo Fortunati", Università di Bologna Statistical depth functions are introduced as a way to provide a center-outward ordering of the sample points in multidimensional space, which can be used for outlier detection, classification, and other exploratory tools. In this work we propose a novel definition of depth function for multivariate data using random directions, which preserves the Mahalanobis distance of the points in the original space. More specifically, the proposed depth function is the expectation of all depths along the potentially infinite random directions, which, in turn, are functions of the point percentiles estimated via parametric or nonparametric models. The proposed method is evaluated through simulated experiments and real data applications, and is shown to be effective in supervised classification problems.