Computing of high breakdown regression estimators without sorting on graphics processing units

We present an approach to computing high-breakdown regression estimators in parallel on graphics processing units (GPU).We show that sorting the residuals is not necessary, and it can be substituted by calculating the median. We present and compare various methods to calculate the median and order statistics on GPUs. We introduce an alternative method based on the optimization of a convex function, and showits numerical superiority when calculating the order statistics of very large arrays on GPUs.