  Quantile classifiers for potentially high-dimensional data are defined by
classifying an observation according to a sum of appropriately weighted
component-wise distances of the components of the observation to the
within-class quantiles. An optimal percentage for the quantiles can be chosen
by minimizing the misclassification error in the training sample.
  It is shown that this is consistent, for $n \to \infty$, for the
classification rule with asymptotically optimal quantile, and that, under some
assumptions, for $p\to\infty$ the probability of correct classification
converges to one. The role of skewness of the involved variables is discussed,
which leads to an improved classifier.
  The optimal quantile classifier performs very well in a comprehensive
simulation study and a real data set from chemistry (classification of
bioaerosols) compared to nine other classifiers, including the support vector
machine and the recently proposed median-based classifier (Hall et al., 2009),
which inspired the quantile classifier.
