A test for the two-sample problem using mutual information

Abstract

For two independently drawn samples from continuous distributions, a statistical test based on the mutual information statistic is proposed for the null hypothesis that both the samples originate from the same population. Asymptotic properties of the test statistic under the null hypothesis of equality is developed. It is demonstrated through simulation that this test is more powerful than the commonly used nonparametric tests in many situations. As an application we discuss the information leak of e-passports. Using the mutual information based test, we detect information leak in a situation where other non-parametric tests fail.