Statistical data depth and the graphics hardware

The notion of 'depth' has been used in statistics as a way to identify the center of the bivariate distribution given by the point set P in R(2). We present a general framework for computing such statistical estimators, that makes extensive use of modern graphics architectures. As a result, we derive improved algorithms for a number of depth measures such location depth, simplicial depth, Oja depth, colored depth, and dynamic location depth. Our algorithms perform significantly better than currently known implementations, outperforming them by at least one order of magnitude and having a strictly better asymptotic growth rate.