  Both the median-based classifier and the quantile-based classifier are useful
for discriminating high-dimensional data with heavy-tailed or skewed inputs.
But these methods are restricted as they assign equal weight to each variable
in an unregularized way. The ensemble quantile classifier is a more flexible
regularized classifier that provides better performance with high-dimensional
data, asymmetric data or when there are many irrelevant extraneous inputs. The
improved performance is demonstrated by a simulation study as well as an
application to text categorization. It is proven that the estimated parameters
of the ensemble quantile classifier consistently estimate the minimal
population loss under suitable general model assumptions. It is also shown that
the ensemble quantile classifier is Bayes optimal under suitable assumptions
with asymmetric Laplace distribution inputs.
