On an Exact and Nonparametric Test for the Separability of Two Classes by Means of a Simple Threshold

Abstract: 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.