Statistical data depths and their local version, an introduction.

Statistical data depth is a growing area in non-parametric statistics, originally developed for the analysis of multidimensional data but useful in other frameworks such as e.g. spherical and functional data. The main applications are a center-outward ordering of the observations, location and scale estimation, classification, clustering and some graphical tools. Statistical local depth functions are a generalization of statistical depth functions and they are used for describing local geometric features and mode(s) in multivariate distributions.

In this seminar, after an introduction on statistical data depths, we illustrate some analytical and statistical properties of the local depths. We show how these functions are a bridge between density functions and depths, we illustrate their theoretical properties and we discuss some applications.