  This paper introduces a statistical test inferring whether a variable allows
separating two classes by means of a single critical value. Its test statistic
is the prediction error of a nonparametric threshold classifier. While this
approach is adequate for univariate classification tasks, it is especially
advantageous for filter-type variable selection. It constitutes a robust and
nonparametric method which may identify important otherwise neglected
variables. It can incorporate the operating conditions of the classification
task. Last but not least, the exact finite sample distribution of the test
statistic under the null hypothesis can be calculated using a fast recursive
algorithm.
