# S. Nagy(KPMS MFF UK): Statistical Data Depth and its Applications

On 2018-02-22 11:00:00 at G205, Karlovo náměstí 13, Praha 2

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, high-dimensional, and even functional

(infinite-dimensional) datasets.

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, high-dimensional, and even functional

(infinite-dimensional) datasets.