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We present and compare various approaches to a classical selection problem onGraphics Processing Units (GPUs). The selection problem consists in selectingthe $k$-th smallest element from an array of size $n$, called $k$-th orderstatistic. We focus on calculating the median of a sample, the $n/2$-th orderstatistic. We introduce a new method based on minimization of a convexfunction, and show its numerical superiority when calculating the orderstatistics of very large arrays on GPUs. We outline an application of thisapproach to efficient estimation of model parameters in high breakdown robustregression.

Parallel calculation of the median and order statistics on GPUs with application to robust regression