In nonparametric statistics the concept of quantiles is of paramount importance.
In multivariate spaces, however, quantiles cannot be defined directly, due to
the lack of natural ordering of points. In the talk we focus on one possible
solution to this problem, using a tool called data depth. Depth is a function
that quantifies the "centrality" of points, with respect to a given probability
distribution. Points with high depth values form the "inner" quantile regions of
the distribution; points of low depth lie on the outskirts of the data cloud. We
discuss approaches to the definition of data depth, and illustrate these in a
series of simple examples. The applications of this methodology include data
visualisation,(robust) estimation, classification, clustering, or outlier
detection for multivariate, highdimensional, and even functional
(infinitedimensional) datasets.
