Alexandre Leblanc

The projection median and its connection to multivariate ranks, medians and depth-weighted averages

In this presentation, I will discuss the concepts of multivariate ranks, depthand outlyingness. I will also describe how multivariate medians can be definedas points of highest depth or multivariate rank, or lowest outlyingness. Forestimating multivariate location, I will describe depth-weighted averages and the Stahel-Donoho estimator, which are robust sample averages with adaptive weights. As an alternative to these computationally intensive methods that areimpractical in high dimensional problems, I will present the projection medianintroduced by Durocher & Kirkpatrick (2005, 2009). Recent results suggest thatthis estimator is an interesting alternative to the other better known robust
methods of estimating multivariate location.
Note: This is based on joint work with S. Durocher (University of Manitoba) and M. Skala  (IT University of Copenhagen).