Milan Merkle: Spatial medians, depth functions and Jensen's inequality

V četrtek, 4. junija 2015, ob 14:30 bo v predavalnici 3.06 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 v Ljubljani predaval prof. dr. Milan Merkle (Univerza v Beogradu).

Povzetek predavanja:

The problem of finding the deepest set of points in a multidimensional data cloud (in the sense of being representative values as a robust alternative to expectations) is much more complex than in dimension one, because there are infinitely many different possibilities to extend the concept of median to higher dimensions. In the talk we are going to discuss so called "type D" depth functions in terminology of Zuo and Serfling (2000), where the most known concept of Tukey depth belongs. The major problem why those ideas have not been widely implemented so far is the absence of efficient algorithms for evaluation of depths in dimensions higher than 2. This is a problem which is per se of interest in Computer Science, and there is also a considerable amount of references in this area, which does not seem to be known to statisticians.

We will present some results from Merkle (2010), as well as a Jensen type inequality with medians in place of means, and we will discuss some applications. An overview of a work in progress will also be presented.