A nonparametric two‐sample test using a general φ‐divergence‐based mutual information

Abstract

Nonparametric two‐sample problems are extremely important for applications in different applied disciplines. We define a general MI based on the φ divergences and use its estimate to propose a new general class of nonparametric two sample tests for continuous distributions. We derive the asymptotic distribution of the estimates of φ‐divergence‐based MI (φDMI) under the assumption of independence in the hybrid setup of one binary and one continuous random variables. Additionally, for finite sample cases, we describe an algorithm for obtaining the bootstrap‐based critical value of our proposed two‐sample test based on the estimated φDMI. We demonstrate through extensive simulations that the proposed class of tests work exceptionally well in many situations and can detect differences where other two‐sample tests fail. Finally, we analyze an application of our proposed tests to assess a solution to information leakage in e‐passport data.