Directional Quantile Classifiers

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 probability of correct classification of the proposed classifier converges to one 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. Supplementary materials for this article are available online.