Multivariate Quantiles

This new paper got me thinking. How often one wishes for a natural notion of multivariate median, or more generally, multivariate quantiles. Had fun learning about centerpoints and Tukey depths.

Multiple-Output Quantile Regression
By: Marc Hallin ; Miroslav Šiman
URL: http://d.repec.org/n?u=RePEc:eca:wpaper:2013/224753&r=ecm
(Skip the first page, which is evidently from a different paper.)