  We introduce classifiers based on directional quantiles. We derive
theoretical results for selecting optimal quantile levels given a direction,
and, conversely, an optimal direction given a quantile level. We also show that
the misclassification rate is infinitesimal if population distributions differ
by at most a location shift and if the number of directions is allowed to
diverge at the same rate of the problem's dimension. We illustrate the
satisfactory performance of our proposed classifiers in both small and high
dimensional settings via a simulation study and a real data example. The code
implementing the proposed methods is publicly available in the R package
Qtools.
